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arXiv · 2207.08313

Exponential Mixing of Vlasov equations under the effect of Gravity and Boundary

Jiaxin Jin·Chanwoo Kim
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Abstract

In this paper, we study exponentially fast mixing induced/enhanced by gravity and stochastic boundary in the kinetic theory of Vlasov equations. We consider the Vlasov equations with and without a vertical magnetic field inside a horizontally-periodic 3D half-space equipped with a non-isothermal diffusive reflection boundary condition of bounded continuous boundary temperature at the bottom. We construct both stationary solutions and global-in-time dynamical solutions in $L^\infty$. We prove that moments of a dynamical fluctuation around the steady solutions decay exponentially fast in $L^\infty$. As a key of this proof, we establish a uniform bound of so-called residual measures independently of the bouncing number of stochastic characteristics, by constructing a continuous stationary outgoing boundary flux which is strictly positive almost everywhere.

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Jiaxin Jin, Chanwoo Kim. 2022-07-17. Exponential Mixing of Vlasov equations under the effect of Gravity and Boundary. https://arxiv.org/abs/2207.08313

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