Abstract: I will present upcoming non-linear stability results concerning the asymptotic behavior of solutions to classical models arising in kinetic theory. First, I will present an asymptotic stability result for the exterior of the Schwarzschild family of black holes as a solution to the Einstein–massless Vlasov system, assuming spherical symmetry. We exploit the normal hyperbolicity of the trapped set in the black hole exterior to obtain decay in time of the energy momentum tensor. I will also speak about an asymptotic stability result for small data solutions to the Vlasov–Poisson system with an unstable trapping potential (joint work with Anibal Velozo).
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