论文标题

在重力和边界的效果下,Vlasov方程的指数混合

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

论文作者

Jin, Jiaxin, Kim, Chanwoo

论文摘要

在本文中,我们研究了Vlasov方程动力学理论中重力和随机边界引起/增强的指数快速混合。我们考虑有和没有垂直磁场的Vlasov方程在水平周期性的3D半空间内,配备了底部有边界连续边界温度的非等温扩散反射边界条件。我们在$ l^\ indty $中构建固定解决方案和全球动态解决方案。我们证明,在$ l^\ infty $中,稳定的解决方案衰减的动态波动的时刻。作为此证明的关键,我们通过构建一个连续的固定式外向式边界通量,建立了所谓的残差措施的统一界限,而与随机特征的弹跳数量无关,几乎无处不在。

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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