Exponential mixing of Vlasov equations under the effect of gravity and boundary
Exponential mixing of Vlasov equations under the effect of gravity and boundary
复制标题
重力和边界作用下 Vlasov 方程的指数混合
DOI：
10.1016/j.jde.2023.04.038
复制
发表时间：
2023
影响因子：
2.4
通讯作者：
Kim, Chanwoo
中科院分区：
文献类型：
--
作者：
Jin, Jiaxin;Kim, Chanwoo
本文研究了Vlasov方程动力学理论中引力和随机边界诱导/增强的指数快速混合。我们考虑了在水平周期三维半空间中有垂直磁场和无垂直磁场的Vlasov方程，该半空间底部具有有界连续边界温度的非等温漫反射边界条件。我们在L∞中构造了稳态解和全局时间动力学解。我们证明了围绕定常解的动力学涨落的矩在L∞中指数快速衰减。作为证明的关键，我们通过构造一个几乎处处严格为正的连续平稳的流出边界流，建立了一个与随机特征的弹跳数无关的所谓剩余测度的统一界.
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∞. We prove that moments of a dynamical fluctuation around the steady solutions decay exponentially fast in L∞. 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.