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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

Stability estimates in Wasserstein distance for some kinetic equations




Date(s) : 26/03/2019   iCal
11h00 - 12h00

In this talk I intend to illustrate the use of Wasserstein distances in the space of probability measures, arising in the context of optimal transportation, in order to obtain stability estimates for some kinetic equations. We shall first recall how this approach allowed to obtain a uniqueness result for weak solutions of the Vlasov-Poisson system with bounded density (G.Loeper, 2005). In a second time we explain how to adapt these ideas in the context of the Vlasov-Navier-Stokes (VNS) system (D.Han-Kwan, E.Miot, A.Moussa and I.M., 2017), which requires to suitably modify the previous approach. Finally, we apply these methods to study the long-time behaviour of the VNS system in the 2D and 3D torus: we prove that the weak solutions of this system converge exponentially fast to a monokinetic profile that we can describe with some detail.

http://ivan.moyano.perso.math.cnrs.fr

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