Stability estimates in Wasserstein distance for some kinetic equations

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Date(s) - 26/03/2019
11 h 00 min - 12 h 00 min


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.

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