(this is (only) an information/added-ref (because rg do not "suggest" it) to my project and not a question, and/but eg see also below or my "answer" below, starting with the tx = "(here is copy of my mel ..." =) https://www.theses.fr/2017PESC1215.pdf = "Qualitative study of the solutions of density-dependent incompressible Navier-Stokes system" =Étude qualitative des solutions du système de Navier-Stokes incompressible à densité variable", Xin ZHANG, thesis29/9/17?
.
= École Doctorale MSTIC Laboratoire d’Analyse et de Mathématiques Appliquées Thèse Présentée pour l’obtention du grade de DOCTEUR DE L’UNIVERSITE PARIS-EST par Xin ZHANG Étude qualitative des solutions du système de Navier-Stokes incompressible à densité variable Spécialité : Mathématiques Soutenue le 29 September 2017 devant un jury composé de : Directeur de thèse DANCHIN Raphaël (Université Paris-Est Créteil) Rapporteur ALAZARD Thomas (l’ENS Paris-Saclay) ZHANG Ping (Institute of Mathematics, AMSS) Président du jury CHEMIN Jean-Yves (Université Pierre et Marie Curie) Examinateur DALIBARD Anne-Laure (Université Pierre et Marie Curie) GALLAGHER Isabelle (Université Paris Diderot) LACAVE Christophe (Université Grenoble Alpes) ...
=========================================
(here is copy of my mel to all the 8 members of the jury and the author of this thesis by Xin Zhang, thesis mainly on striated regs, vortex patches etc=) *6nv18/ = "VP 2d 3d nd= chemin (2d) / serfati (2+3+nd) / bertozzi (&constantin) (2d)/ gamblin & straymond (3d) / danchin (2+3+nd) etc". from SERFATI philippe (see researchgate for full texts etc) .(PhD+Ec.Norm.Sup.-PS+AGREGATION in MATHS. 245 citations by 125 international university authors) = to all the 8 members of the jury and the author of the thesis (see file below or the adweb = https://www.researchgate.net/deref/https%3A%2F%2Fwww.theses.fr%2F2017PESC1215.pdf) = Xin ZHANG Étude qualitative des solutions du système de Navier-Stokes incompressible à densité variable Spécialité : Mathématiques Soutenue le 29 September 2017 devant un jury composé de : Directeur de thèse DANCHIN Raphaël (Université Paris-Est Créteil) Rapporteur ALAZARD Thomas (l’ENS Paris-Saclay) ZHANG Ping (Institute of Mathematics, AMSS) Président du jury CHEMIN Jean-Yves (Université Pierre et Marie Curie) Examinateur DALIBARD Anne-Laure (Université Pierre et Marie Curie) GALLAGHER Isabelle (Université Paris Diderot) LACAVE Christophe (Université Grenoble Alpes) = ([email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]).
--on the 130 refs of this thesis, at least +-20/25% are on Vortex patches (by 25/30 authors), 2d, 3d, nd, general and regular plus VP2d with cusps (thesis where my name or my works do not appear, even on these subjects)= i recall eg that i have always in 2018, even by points taken separately, the strongest results in vp2d loc in t, vp2d global in t (but jy chemin and bertozzi&constantin were first for vp2d glob), the very firsts and still the strongest results in vp3d and vpnd, n>=3, and eg i have 4 works on vp with cusps and +-10 works or sub-chapters of my thesis on VP and +-5 of them published, +-still far the strongests in 2018. here is below, some of my short texts detailling some of this (some others exist also), and it is said and intend to be said, repeatedly, to all authors on VP, and eg (already) to (some of) you all (and txs eg compiled on my data = ""rg-texts on papers on anisotropies, morrey spaces and elliptic problems and holomorphies on opens and vortex patches machineries etc, 2017-18 from Serfati-philippe October 2017 DOI: 10.13140/RG.2.2.35956.04482/"" and/or foundable in diverse places of my profiles (eg) on RG etc) = tell me what you will do (eg on VP 3d and/or VPnd, n>=3, where i was the first author)
=====================================
"VP2d glob and loc in t = results, forces, anteriorities, dates etc. chemin jy /serfati p / bertozzi&constantin etc" = (intend to be) said to researchers on VP2d glob and loc in t = oct 2018= from SERFATI philippe (see researchgate for full texts etc) .(PhD+Ec.Norm.Sup.-PS+AGREGATION in MATHS. 245 citations by 125 international university authors) =
because you cite some papers on contour dynamics and (stratified/striated foliated) vortex patches in 2d, and i have a lot of works on VP, see eg them in full texts on researchgate profile =1/ for globality in t of VP2d, if you do cite jy-chemin/"persist.." and/or bertozzi&C then you HAVE at least to cite my CRAS94/vp2glob (=Une preuve directe d'existence globale des vortex patches 2D Jan 1994 Philippe Serfati) with the same force than chemin/persist (then him and me far stronger me than BC, see eg 3/) and furthermore i am "short, elementary and complete/self-contained and eg with NO paradiff" (but i am posterior to C/P and BC= my position is then in force and/or importance n°= 2 or 1 and not at all 3), 2/ as jy chemin and his students and others authors say it later in their books and papers and as the editor of my cras authorise me to say it.3/ chemin and me, have an infinity of Cm+s strata (and general discontinuous data Cm+s on them), all m, and BC only one unique C1+s (or Cm+s?, see below) stratum and only a constant by pieces discontinuous data out of this one stratum and furthermore BC is NOT self-contained because they (say they) admit a non-trivial lemma due to cotlar (with the remarks = chemin and me, use for general m, their previous results local in t, eg for me my ch4b3-91 of thesis9-92, in nd, all n, and him for n=2 but i don't know for the thesis by bertozzi, if she have m=1 or all m and non?-constant VP/contour dynamics).4/ the strongest vp2glob-in-t, always in 2018, is one of my theorems (ie a part of my th3/2.b).) in "Vortex patches dans Rn et régularité stratifiée pour le laplacien"/Oct 1993 (see full tx on my profile on rg), eg on every separate points = on transverse regularities far more general than those by jy chemin and anyone else even in 2018 (2d and nd), on lagrangian holomorphies/analyticities in t,r, (and functional ones on) uo, edos, on anisotropic regs for singular integrals and iterate commutators, then all this on lR^n, all n etc,5/ on local in t, vp2d, i was in "vp bidi"/2-1990/ch4a of my thesis9-92, first and simultaneous and independant with and from jy chemin/loc-t-vp2d/1or6-90 (see eg p. gerard/bourbaki1992, http://www.numdam.org/article/SB_1991-1992__34__411_0.pdf), him foliated, lagrangian t-C°°, with an epsilon loss in x-reg, me contour dynamic nearly circular but with lag. t-analyticity with no epsilon loss in x-reg (see also the thesis1991 by a. bertozzi but i don't have it in hand).6/ tell me what you will do.
=========================================
"VPnd, all n>=3 or n=3 = results, forces, anteriorities, dates etc. serfati p / gamblin-stRaymond / danchin / etc" =
on VPnd = (intend to be) said to researchers on VP = rct*9+13/10/18 = from SERFATI philippe (PhD+Ec.Norm.Sup.-PS+AGREGATION in MATHS. 245 citations by 125 international university authors) =(intend to be) said to researchers on VP =
= i reput below my tx on VP3d and nd, all n>=3, and i still say to you my remarks on your/this last version(s) of your VPnd-paper(s), n=3 or n>=3 = you have to say that, for all n (and even also restricted to 3d), i am and i was and i was the 1st in date on VP3d and VPnd, all n>=3 and (in ch4b/3-91 of thesis (at the time, only VP2d and jy chemin existed then, only for +-one year and 2d only (with also on VP2d on one single curve, my vpbidi2-90/2d/ch4a and bertozzi/2d/thesis/91)) etc and eg its extended rework/10-93postdoc (and not its "correction") ...) i was and i am still the strongest in 2018 on them (even by points taken separately. my cras94reg.strat.euler3d.gd.tps contains only partial things = a partial "posterior" "announcement" of this ch4b (and ch4a), and in VP, only a full proof of an only axisym (but t-glob) particular VP-result, only on 3d, with no extra higher (or no the most general transverse) x-regs and no lagrangian t-analytic t-regs or no (t,r,uo,EDOs) scalar and functional lag-holomorphies etc)
--tell me what you will do (eg because you treat, describe, cite etc papers and results etc on VPnd, all n>=3 or n=3, then you have to cite my papers on VPnd, all n>=3 or n=3) =
+Vortex Patches in lR^n, n in [3,4,5, ... [ and n=3 (and not n=2)= forces and anteriorities and authors and works. ..see also eg other previous §s on comments (rg, scirate..) on eg papers by bae&Kelliher, danchin, sueur, fanelli, paicu, dutrifoy, c.huang, gamblin& x.StRaymond, P. Zhang, Q. J.Qiu, X.Zhang, x.Liao, L. Yanlin etc =24/8/18 = on authors on VP nd, all n, or n =3 = on VP nd, all n (and so eg n in [3,4,5, ... [, where I was absolutely present, the only one and the first in dates (and what is more, always the strongest in 2018, even by points / criteria taken separately), which all must recognize and say, eg all n, all Cm+s, all m, on transverse regularities, holomorphies/analyticities in t, r (functional ones in) uo, edos and these anisotropic regs for singular integrals and iterate commutators etc), in my ch4b / 3-91 (of thesis9-92) and its extended reworking ""Vortex patches dans Rn et régularité stratifiée pour le laplacien""/ 10-93 (:"" Vortex patches in Rn and stratified regularity for the Laplacian ""), all the 3, previous to 32 (/ 14) and 1 month(s) to gamblin & X.St-Raymond / vp3d / 11-93 (the only 1sts after me in Vp nd, n in [3,4,5, ... [), I described for VP Rn, all n and thus (eg said to bae&kelliher) in Rn, all n, eg also we have already in ch4b (with as an example biot-savart :) D2 (lap ^ -1) = finite sum of I times P, where I are operators (non-local) isotropic Cm + s (and sending and raising an anisotropic space towards the iso-Cm + s) and P explicit, basic (and thus discontinuous) pointwise operators, being only rational fractions of elements of this anisotropic space = this in Rn, all n (and not only, as eg bae & kelliher to read them, n = 2 or 3 alone and with only references to my 2 cras94 v2dglob and v3daxiglob, the last one is an announcement of only a part of the ch4b/91+ch4a/90 of thesis92 plus 2 full proved non-signed (particular) axi3d results and eg Gamblinx/StR (paper, ch and/of thesis) always cited by all, had also its own CRAS of announcement, almost never cited (in "replacement")).
.rct 24/9/18 = the thesis by gamblin dates from 11-93 but its chp / vp3d /a-preprint/pre-version? from 01-93 ((but said submitted in 11-93 by the review, 10 months latter)), whose (2) only new results are the t-global cases in axi iso-quasilip and axiVp, curl> 0, all because it is said in my cras94reg.strat.lap.euler said submitted in 01-93, which improves these 2 points to the unsigned case, this chp is weaker on everything and is posterior, the 2 to my ch4b /10-91 of my thesis 9-92, ch4b, which my rework & extension / 10-93 does not owe anything to the ch/vp3d/gamblin/, that is the reason why I do not quote nor describe it (what I do, at the opposite, in my cras, and even beyond these 2 points, then there with no obligation, seen that my ch4b is anterior to and contains his ch, except his 2axi results).
--https://www.researchgate.net/profile/Philippe_Serfati
=======================================================
--my 4 works on VP (2+3+nd) with cusps, regular, irregular, singular, generalized =// Solutions non bornées de l'équation d'Euler Incompressible 3D et singularités interfaciques Article Full-text available Feb 1999 Philippe Serfati // Singularité logarithmique confinée dans un cusp régulier et équation d'Euler 2D Article Full-text available Dec 1998 Philippe Serfati // Stratifications planes superposées singulières et équation d'Euler 2D à temps grand Article Full-text available Oct 1998 Philippe Serfati// Stratifications superposées singulières. analyse harmonique. commutateurs et équation d'Euler sur Rn Article Full-text available Jul 1998 Philippe Serfati //
==========================================
--- on splash discontinuities, nd-cusps and gains for them in term of harmonic analysis =..., my last 4 papers 1998-99 on it and the last 2 ("2d sing cusp log" and "3d underlip sing interfaciques") deal with more singular situations (unless I'm mistaken) than usually do = i see cusps as superposition of 2 VP with tangent contacts/ intersections of their boundaries = more singular sols, ie VPs more singular near their (more singular) contacts, non-boundedness of/and added singularities near the contacts, on the gradients g etc of the boundaries and also on the functions f defined between these boundaries= "sing log cusp 2d" (f=log, regular cusp, ie g reg), "3d sing interfaciques" (exp(c.lfl^µ) in L1 and exp(c.lgl^µ') in L1, c and µ,µ'>0)), these situations have a gain in term of harmonic analysis = eg, lD2(Lap-1)*f lp < p^b Clflp, p-->oo, with b (>0 or =0) better than the usual b=1, ie b = 0 for a regular cusp (or inside space between 2 tangents hypersurfaces where f has its support and is in an Lp, f finite) or b
(here is copy of my mel to all the 8 members of the jury and the author of this thesis by Xin Zhang, thesis mainly on striated regs, vortex patches etc=) *6nv18/ = "VP 2d 3d nd= chemin (2d) / serfati (2+3+nd) / bertozzi (&constantin) (2d)/ gamblin & straymond (3d) / danchin (2+3+nd) etc". from SERFATI philippe (see researchgate for full texts etc) .(PhD+Ec.Norm.Sup.-PS+AGREGATION in MATHS. 245 citations by 125 international university authors) = to all the 8 members of the jury and the author of the thesis (see file below or the adweb = https://www.researchgate.net/deref/https%3A%2F%2Fwww.theses.fr%2F2017PESC1215.pdf) = Xin ZHANG Étude qualitative des solutions du système de Navier-Stokes incompressible à densité variable Spécialité : Mathématiques Soutenue le 29 September 2017 devant un jury composé de : Directeur de thèse DANCHIN Raphaël (Université Paris-Est Créteil) Rapporteur ALAZARD Thomas (l’ENS Paris-Saclay) ZHANG Ping (Institute of Mathematics, AMSS) Président du jury CHEMIN Jean-Yves (Université Pierre et Marie Curie) Examinateur DALIBARD Anne-Laure (Université Pierre et Marie Curie) GALLAGHER Isabelle (Université Paris Diderot) LACAVE Christophe (Université Grenoble Alpes) = ([email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]).
--on the 130 refs of this thesis, at least +-20/25% are on Vortex patches (by 25/30 authors), 2d, 3d, nd, general and regular plus VP2d with cusps (thesis where my name or my works do not appear, even on these subjects)= i recall eg that i have always in 2018, even by points taken separately, the strongest results in vp2d loc in t, vp2d global in t (but jy chemin and bertozzi&constantin were first for vp2d glob), the very firsts and still the strongest results in vp3d and vpnd, n>=3, and eg i have 4 works on vp with cusps and +-10 works or sub-chapters of my thesis on VP and +-5 of them published, +-still far the strongests in 2018. here is below, some of my short texts detailling some of this (some others exist also), and it is said and intend to be said, repeatedly, to all authors on VP, and eg (already) to (some of) you all (and txs eg compiled on my data = ""rg-texts on papers on anisotropies, morrey spaces and elliptic problems and holomorphies on opens and vortex patches machineries etc, 2017-18 from Serfati-philippe October 2017 DOI: 10.13140/RG.2.2.35956.04482/"" and/or foundable in diverse places of my profiles (eg) on RG etc) = tell me what you will do (eg on VP 3d and/or VPnd, n>=3, where i was the first author)
=====================================
"VP2d glob and loc in t = results, forces, anteriorities, dates etc. chemin jy /serfati p / bertozzi&constantin etc" = (intend to be) said to researchers on VP2d glob and loc in t = oct 2018= from SERFATI philippe (see researchgate for full texts etc) .(PhD+Ec.Norm.Sup.-PS+AGREGATION in MATHS. 245 citations by 125 international university authors) =
because you cite some papers on contour dynamics and (stratified/striated foliated) vortex patches in 2d, and i have a lot of works on VP, see eg them in full texts on researchgate profile =1/ for globality in t of VP2d, if you do cite jy-chemin/"persist.." and/or bertozzi&C then you HAVE at least to cite my CRAS94/vp2glob (=Une preuve directe d'existence globale des vortex patches 2D Jan 1994 Philippe Serfati) with the same force than chemin/persist (then him and me far stronger me than BC, see eg 3/) and furthermore i am "short, elementary and complete/self-contained and eg with NO paradiff" (but i am posterior to C/P and BC= my position is then in force and/or importance n°= 2 or 1 and not at all 3), 2/ as jy chemin and his students and others authors say it later in their books and papers and as the editor of my cras authorise me to say it.3/ chemin and me, have an infinity of Cm+s strata (and general discontinuous data Cm+s on them), all m, and BC only one unique C1+s (or Cm+s?, see below) stratum and only a constant by pieces discontinuous data out of this one stratum and furthermore BC is NOT self-contained because they (say they) admit a non-trivial lemma due to cotlar (with the remarks = chemin and me, use for general m, their previous results local in t, eg for me my ch4b3-91 of thesis9-92, in nd, all n, and him for n=2 but i don't know for the thesis by bertozzi, if she have m=1 or all m and non?-constant VP/contour dynamics).4/ the strongest vp2glob-in-t, always in 2018, is one of my theorems (ie a part of my th3/2.b).) in "Vortex patches dans Rn et régularité stratifiée pour le laplacien"/Oct 1993 (see full tx on my profile on rg), eg on every separate points = on transverse regularities far more general than those by jy chemin and anyone else even in 2018 (2d and nd), on lagrangian holomorphies/analyticities in t,r, (and functional ones on) uo, edos, on anisotropic regs for singular integrals and iterate commutators, then all this on lR^n, all n etc,5/ on local in t, vp2d, i was in "vp bidi"/2-1990/ch4a of my thesis9-92, first and simultaneous and independant with and from jy chemin/loc-t-vp2d/1or6-90 (see eg p. gerard/bourbaki1992, http://www.numdam.org/article/SB_1991-1992__34__411_0.pdf), him foliated, lagrangian t-C°°, with an epsilon loss in x-reg, me contour dynamic nearly circular but with lag. t-analyticity with no epsilon loss in x-reg (see also the thesis1991 by a. bertozzi but i don't have it in hand).6/ tell me what you will do.
=========================================
"VPnd, all n>=3 or n=3 = results, forces, anteriorities, dates etc. serfati p / gamblin-stRaymond / danchin / etc" =
on VPnd = (intend to be) said to researchers on VP = rct*9+13/10/18 = from SERFATI philippe (PhD+Ec.Norm.Sup.-PS+AGREGATION in MATHS. 245 citations by 125 international university authors) =(intend to be) said to researchers on VP =
= i reput below my tx on VP3d and nd, all n>=3, and i still say to you my remarks on your/this last version(s) of your VPnd-paper(s), n=3 or n>=3 = you have to say that, for all n (and even also restricted to 3d), i am and i was and i was the 1st in date on VP3d and VPnd, all n>=3 and (in ch4b/3-91 of thesis (at the time, only VP2d and jy chemin existed then, only for +-one year and 2d only (with also on VP2d on one single curve, my vpbidi2-90/2d/ch4a and bertozzi/2d/thesis/91)) etc and eg its extended rework/10-93postdoc (and not its "correction") ...) i was and i am still the strongest in 2018 on them (even by points taken separately. my cras94reg.strat.euler3d.gd.tps contains only partial things = a partial "posterior" "announcement" of this ch4b (and ch4a), and in VP, only a full proof of an only axisym (but t-glob) particular VP-result, only on 3d, with no extra higher (or no the most general transverse) x-regs and no lagrangian t-analytic t-regs or no (t,r,uo,EDOs) scalar and functional lag-holomorphies etc)
--tell me what you will do (eg because you treat, describe, cite etc papers and results etc on VPnd, all n>=3 or n=3, then you have to cite my papers on VPnd, all n>=3 or n=3) =
+Vortex Patches in lR^n, n in [3,4,5, ... [ and n=3 (and not n=2)= forces and anteriorities and authors and works. ..see also eg other previous §s on comments (rg, scirate..) on eg papers by bae&Kelliher, danchin, sueur, fanelli, paicu, dutrifoy, c.huang, gamblin& x.StRaymond, P. Zhang, Q. J.Qiu, X.Zhang, x.Liao, L. Yanlin etc =24/8/18 = on authors on VP nd, all n, or n =3 = on VP nd, all n (and so eg n in [3,4,5, ... [, where I was absolutely present, the only one and the first in dates (and what is more, always the strongest in 2018, even by points / criteria taken separately), which all must recognize and say, eg all n, all Cm+s, all m, on transverse regularities, holomorphies/analyticities in t, r (functional ones in) uo, edos and these anisotropic regs for singular integrals and iterate commutators etc), in my ch4b / 3-91 (of thesis9-92) and its extended reworking ""Vortex patches dans Rn et régularité stratifiée pour le laplacien""/ 10-93 (:"" Vortex patches in Rn and stratified regularity for the Laplacian ""), all the 3, previous to 32 (/ 14) and 1 month(s) to gamblin & X.St-Raymond / vp3d / 11-93 (the only 1sts after me in Vp nd, n in [3,4,5, ... [), I described for VP Rn, all n and thus (eg said to bae&kelliher) in Rn, all n, eg also we have already in ch4b (with as an example biot-savart :) D2 (lap ^ -1) = finite sum of I times P, where I are operators (non-local) isotropic Cm + s (and sending and raising an anisotropic space towards the iso-Cm + s) and P explicit, basic (and thus discontinuous) pointwise operators, being only rational fractions of elements of this anisotropic space = this in Rn, all n (and not only, as eg bae & kelliher to read them, n = 2 or 3 alone and with only references to my 2 cras94 v2dglob and v3daxiglob, the last one is an announcement of only a part of the ch4b/91+ch4a/90 of thesis92 plus 2 full proved non-signed (particular) axi3d results and eg Gamblinx/StR (paper, ch and/of thesis) always cited by all, had also its own CRAS of announcement, almost never cited (in "replacement")).
.rct 24/9/18 = the thesis by gamblin dates from 11-93 but its chp / vp3d /a-preprint/pre-version? from 01-93 ((but said submitted in 11-93 by the review, 10 months latter)), whose (2) only new results are the t-global cases in axi iso-quasilip and axiVp, curl> 0, all because it is said in my cras94reg.strat.lap.euler said submitted in 01-93, which improves these 2 points to the unsigned case, this chp is weaker on everything and is posterior, the 2 to my ch4b /10-91 of my thesis 9-92, ch4b, which my rework & extension / 10-93 does not owe anything to the ch/vp3d/gamblin/, that is the reason why I do not quote nor describe it (what I do, at the opposite, in my cras, and even beyond these 2 points, then there with no obligation, seen that my ch4b is anterior to and contains his ch, except his 2axi results).
--https://www.researchgate.net/profile/Philippe_Serfati
=======================================================
--my 4 works on VP (2+3+nd) with cusps, regular, irregular, singular, generalized =// Solutions non bornées de l'équation d'Euler Incompressible 3D et singularités interfaciques Article Full-text available Feb 1999 Philippe Serfati // Singularité logarithmique confinée dans un cusp régulier et équation d'Euler 2D Article Full-text available Dec 1998 Philippe Serfati // Stratifications planes superposées singulières et équation d'Euler 2D à temps grand Article Full-text available Oct 1998 Philippe Serfati// Stratifications superposées singulières. analyse harmonique. commutateurs et équation d'Euler sur Rn Article Full-text available Jul 1998 Philippe Serfati //
==========================================
--- on splash discontinuities, nd-cusps and gains for them in term of harmonic analysis =..., my last 4 papers 1998-99 on it and the last 2 ("2d sing cusp log" and "3d underlip sing interfaciques") deal with more singular situations (unless I'm mistaken) than usually do = i see cusps as superposition of 2 VP with tangent contacts/ intersections of their boundaries = more singular sols, ie VPs more singular near their (more singular) contacts, non-boundedness of/and added singularities near the contacts, on the gradients g etc of the boundaries and also on the functions f defined between these boundaries= "sing log cusp 2d" (f=log, regular cusp, ie g reg), "3d sing interfaciques" (exp(c.lfl^µ) in L1 and exp(c.lgl^µ') in L1, c and µ,µ'>0)), these situations have a gain in term of harmonic analysis = eg, lD2(Lap-1)*f lp < p^b Clflp, p-->oo, with b (>0 or =0) better than the usual b=1, ie b = 0 for a regular cusp (or inside space between 2 tangents hypersurfaces where f has its support and is in an Lp, f finite) or b
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