Effective pointwise minorations for Nd integral nonlocal evolving eqs, sols/kernels/integrands+applications to Euler2+?3d+Vortex-Patches-cusp/contact?

*28nv18/ = ""nd integral nonlocal evolving eqs, effective (signed pointwise) (x,t)-mino(/majo-)rations of 1d-components of sols/kernels/integrands, applications to Euler2+?3d and VP-cusps-on-Rn/vortex-patches-with-contacts-with-fixed-boundaries.28nv18"". (intended to be said) to researchers on the subjects below (see [BaCh] at the end here)= 1/ one of your field here (in this and others works by you etal) is the one, always quite active (and very interesting and +-new with new and specific kinds of techniques and manipulations and terms..), of effective punctual minoration bounds in time of L°°x bounds (are there works eg on x-means instead of x-L°°, ie in I(t) = integ_Q(t) lf(x,t)ldx/lQ(t)l >= Cexp(Ct), C>0, t>=0 (f=rot etc, I(t) =< lf(t)l_x,oo..), where Q(t) is an x-domain varying/decreasing (for the inclusion of sets) in t eg with lQ(t)l ->0+ when t goes to +oo (eg Q= B(xo,R(t)) (intersected with the fixed domain omega), R(t) = c exp(-c't), c,c'>0) or involving some other integral/"density" terms/sets (better than {xo}) of points x of "explosions"/optimality ?) and you do, in a first step, a lot of strong specific preparation (and oriented) work to then be able, in a 2nd step, to use and adapt these techniques and have these kind of results of effective minorations = people on VP with cusps etc (eg danchin, chemin, me etc) dont do this strong preparation work (in 1st step) and absolutely cant (and cant pretend) absolutely have your effective minorations, without extra strong works and adaptations (not done wet), but, 2/ you can't deny that on the strict level of t-existences (ie in the qualitative level of this 1st step only), local or global in t, that results on VP with cusps and those on VP with tangent contacts with fixed domains (seen as static VPs) are very near (and the seconds are particular cases of the firsts with some little +-easy adaptations, eg in adding a source/force term at the eqs, with the +- same reg that the one of the sols (then with +-no pb eg in the fixed point or the passage to the limit, creating the sols), term uses to fix some parts/branches of the VPs and their boundaries, then these parts become static), 3/ a lot of authors cite chemin/persistence and bertozzi&Constantin and (nevertheless and often) not me (CRAS94vp2dglob in t)= it is not acceptable in any cases. this, independently of the fact that these authors use or not cheminP and/or BeCo, eg when they are paradiff (ie like ChPe) they cite BeCo or some others are "simple real analysis" one-contour-dynamics (like BeCo and +-you) and cite the far stronger foliated-CP (and i am "simple real analysis" and/but i have the strict level of maths force, than the far stronger foliated-CP (and eg on my last "sols euler3d nonbornées sing interfaciques"/99, i have (in 2d "projection") irregular cusps at their tops (or irregular "tangent" contacts. "irregular" = for all t, all the geometric terms (of the cusp) explode in x-reg near the tops) with unbounded sols (eg curls) and functions in approaching these tops. in 2d with unbounded curl but with a regular cusp, see my "sols 2d euler confinee sing cusp" and where the curl is also regular see in t loc/nd and glob/2d, my 2 "strat sup sing an harmo commut euler Rn" and "strat planes sup sing euler 2d glob"). 4/ and of course your frame of effective punctual minoration bounds in time, with careful and non usual manipulations and estimations (eg minorations etc) pointwisely (also in x) of (and each of) all the 1d components of multidimensional (matricial etc) nonlocal integral operators, depending on the (local) one-sign of their 1d components of kernels and integrands, this frame is a very serious (and perhaps one of the major and/or the most natural, seen from this day) candidate for a (future) good angle of attack and/or atleast advances on the millenium pb, ie incompressible euler 3d eqs explode in finite time or the opposite etc eg on their effective t-growths, eg on 3d particular sols or 3d axi ones with swirl (when nothing is still known at large t) where here also the scalarity (and/or sign and/or constance) of some data (ie (ortho-)radial curl etc) is still existing, natural and important. furthermore, in this (future) intention (and in your own present ones), VP (as a contour dynamics) permits on your frame, to have a (2d) nontrivial curl (for all time) with only always not more than two values, one and zero, separated by a regular curve (then the "only" major unknown/evolving data, with its open empty, ie a good "thin/poor" set for the intentions said higher) with zones of contact with a fixed domain, zones where particles are more trapped and constraign-ed/able than inside the domain (ie far from its boundary), and then where there, more (punctual) +-exact and special etc behaviors are more possible (eg also physically), obtenable and provable (with the help also sometimes, of t-preserved x-symmetries)... 5/ tell me what you will do. --from Philippe Serfati PhD+Ec.Norm.Sup.-PS+AGREGATION in MATHS. 245 citations by 125 international university authors, see researchgate etc. --refs=  see eg, for its (+-1st in date) included effective counterexample, the descendances of [BaCh] = ""Bahouri, H., & Chemin, J. Y. (1994). Équations de transport relatives á des champs de vecteurs non-lipschitziens et mécanique des fluides. Archive for rational mechanics and analysis, 127(2), 159-181."".

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former titles = //Nd nonlocal evolving eqs+signed pointwise (x,t)-minorations of components of sol/kernel/integrand+applications?to Euler3d+VortexPatches-cusp/contacts?//

""nd integral nonlocal evolving eqs, (signed) pointwise (x,t)-mino(/majo-)rations of 1d-components of sols/kernels/integrands, applications? to Euler3d and VP-cusps-on-Rn/vortex-patches-with-contacts-with-fixed-boundaries.28nv18""

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Nd nonlocal evolving eqs+effective signed pointwise (x,t)-minorations for sol/kernel/integrand+applications to Euler2+?3d+Vortex-Patches-cusp/contact?