Vector field methods for kinetic equations with applications to classical and relativistic systems

Smulevici, Jacques

Séminaire Laurent Schwartz — EDP et applications (2016-2017), Exposé no. 3, 10 p.

The aim of this talk is to present an extension of the vector field method of Klainerman, which is typically applied in the context of non-linear wave equations, to the case of kinetic equations of Vlasov type. We first describe how our method yields sharp decay estimates for velocity averages for the linear classical and relativistic transport equations and then explain how it can be applied to various models of mathematical physics, such as the Vlasov-Poisson, Vlasov-Nordström and Vlasov-Einstein systems.

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