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arXiv · 2307.14271

On nonlinear Landau damping and Gevrey regularity

Christian Zillinger
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Abstract

In this article we study the problem of nonlinear Landau damping for the Vlasov-Poisson equations on the torus. As our main result we show that for perturbations initially of size $\epsilon>0$ and time intervals $(0,\epsilon^{-N})$ one obtains nonlinear stability in regularity classes larger than Gevrey $3$, uniformly in $\epsilon$. As a complementary result we construct families of Sobolev regular initial data which exhibit nonlinear Landau damping. Our proof is based on the methods of Grenier, Nguyen and Rodnianski.

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Christian Zillinger. 2023-07-26. On nonlinear Landau damping and Gevrey regularity. https://arxiv.org/abs/2307.14271

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