for information on Point Vortex System to the rg "Project Point Voritces on the surface of a sphere Takashi Sakajo Paul K. Newton" = 2 general theorical maths results on approximation of general finite Point Vortex System in R2 from SERFATI.ph. 2 papers on PVS, one here given from serfati philippe (rct 21-8-17: the 2nd given here: "Borne en temps des caractéristiques de l’Equation d’Euler 2D à tourbillon positif et localisation pour le modèle point-vortex", see its 2017-abstract on my profile)= "Tourbillons -presque- mesures spatialement bornés et équation d'Euler 2D" June 1998 Philippe Serfati on rg (given here). extract from (abstract 2017) Considering the point vortex model for the 2D Euler equation, we prove that the approximate Dirac are localized in Ɛ"-domains (Ɛ"=Ɛ'log(p)(1/Ɛ+e). Ɛ'² =Ɛ), Ɛ ->0+, on each [0,T], if, initially, they are so in Ɛ-domains and are bounded only by Cst.exp(p)(1/Ɛ), where exp(p) and log(p)(.+e) are any p-iterative composed of exponential and log(.+e), p arbitrary. This result and some of those from our other "Borne en temps des caractéristiques de l’Equation d’Euler 2D à tourbillon positif et localisation pour le modèle point-vortex" [where L°° bounds dependance is, mostly importantly, also very weak: LINEARLY in log(p)(e+lvortexlLoo) and a slightly weaker result on the point vortex model where exp(p) and log(p)(.+e) here are replaced by powers of Ɛ of arbitrary small exponents] allow us to make three conjectures: 1) positive measure vortex remains spatially bounded for all [0,T], 2) two differently signed measures vortex, initially separated, remain so for short T (and conclusion of 1) holds), 3) Delort's convergence theorem holds in situation 2). ----- on PVS = my precisely targeted (3rd) result on point vortex system (in the 3 results in "Borne en temps des caractéristiques de l’Equation d’Euler 2D à tourbillon positif et localisation pour le modèle point-vortex") is extremely rarely cited (:by one or very few papers of marchioro (etal)), as PVS result, and never cited for its/my-own improvement in my further paper, never cited = "Tourbillons -presque- mesures spatialement bornés et équation d'Euler 2D", my (3rd) result and my improvement on PVS, being still the strongest ones (even in 2017), to our knowledge (for example, marchioro (etal) with only powers of Ɛ of FIXED exponents but in 1998, there is "simultaneously and independently" (at least for me) to my first "borne en temps etc" (and my other "tourbillon etc"), the weaker to both "borne" and a fortiori, "tourbillon" = "Marchioro, C. (1998). On the localization of the vortices. Bollettino dell'Unione Matematica Italiana, 1(3), 571-584.", where L°° bounds for diracs are initially in cst/Ɛ^k (:as in "borne" but stronger in "tourbillon": cst.exp(p)(1/Ɛ), any p), for ANY k>0, and t-diameters in cst Ɛ^a, 0
.In short on pvs = IF you cite MPbook90' and/or/for-the results in MP93 and/or M98 (local vortices) and/or papers by Turckington motivating/cited-by these 3, then you HAVE to cite my 2 papers ="borne etc"/pvs/98 (strictly better than these 4 (and +) and all authors/papers still in 2019, eg µ 0 FIXed, ie a polynomial dependance of fixed degree, in lrotu (0) loo).- the second R2 (of "borne ...") very rarely quoted or described, but iftimie / 2007, p126 (cf lower) recognizes it as mine and mine alone = the regular N e-approximations signed, e > 0 of a system of N vortex points, of bounds L °° in cst / e ^ k, ALL k> 0 to t null, are, over all [0, T], at distances
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