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dc.contributor.authorMischler, Stéphane
dc.contributor.authorHauray, Maxime
HAL ID: 8012
dc.contributor.authorFournier, Nicolas
dc.date.accessioned2012-12-12T14:32:17Z
dc.date.available2012-12-12T14:32:17Z
dc.date.issued2014
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10705
dc.language.isoenen
dc.subjectEntropy dissipationen
dc.subjectFisher informationen
dc.subjectPropagation of Chaosen
dc.subjectStochastic particle systemsen
dc.subject2D Navier-Stokes equationen
dc.subject.ddc515en
dc.titlePropagation of chaos for the 2D viscous vortex modelen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire d'Analyse, Topologie, Probabilités (LATP) http://www.latp.univ-mrs.fr CNRS : UMR6632 – Université de Provence - Aix-Marseille I – Université Paul Cézanne - Aix-Marseille III;France
dc.contributor.editoruniversityotherLaboratoire d'Analyse et de Mathématiques Appliquées (LAMA) http://umr-math.univ-mlv.fr/ Université Paris-Est Marne-la-Vallée – Université Paris XII - Paris Est Créteil Val-de-Marne – CNRS : UMR8050 – Fédération de Recherche Bézout Université de Paris-Est - Marne-la-Vallée, Cité Descartes, Bâtiment Copernic, 5 bd Descartes, 77454 Marne-la-Vallée Cedex 2, Lab Anal & Math Appl,;France
dc.description.abstractenWe consider a stochastic system of $N$ particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly stronger result : the propagation of chaos of the stochastic paths towards the solution of the expected nonlinear stochastic differential equation. Moreover, the convergence holds in a strong sense, usually called entropic (there is no loss of entropy in the limit). The result holds without restriction (but positivity) on the viscosity parameter. The main difficulty is the presence of the singular Biot-Savart kernel in the equation. To overcome this problem, we use the dissipation of entropy which provides some (uniform in $N$) bound on the Fisher information of the particle system, and then use extensively that bound together with classical and new properties of the Fisher information.en
dc.relation.isversionofjnlnameJournal of the European Mathematical Society
dc.relation.isversionofjnlvol16
dc.relation.isversionofjnlissue7
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages1423–1466
dc.relation.isversionofdoihttp://dx.doi.org/10.4171/JEMS/465
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00762286en
dc.relation.isversionofjnlpublisherEuropean Mathematical Society
dc.subject.ddclabelAnalyseen
dc.description.submittednonen


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