论文标题
弗拉索夫 - 波森方程的边界问题的不均匀稳定解决方案的非线性渐近稳定性
Nonlinear asymptotic stability of inhomogeneous steady solutions to boundary problems of Vlasov-Poisson equation
论文作者
论文摘要
我们考虑了一个无碰撞颗粒的合奏，它们通过牛顿的重力定律的吸引力或库仑定律的静电排斥，在水平周围的3D半空间中的背景下降下，其在边界上的流入分布在水平有限的3D半空间中相互相互作用。我们研究了其通用稳态的非线性渐近稳定性，在弗拉索夫 - 波桑方程的动力学PDE理论中。我们构建了Lipschitz连续的无均匀稳态，并在加权Sobolev拓扑结构中相对于这些稳态的小扰动，建立了这些稳态的快速渐近稳定性。在此证明中，我们在稳态的速度中使用Lipschitz的连续性至关重要。此外，我们为稳定和动态问题建立了良好的和规律性的估计。
We consider an ensemble of mass collisionless particles, which interact mutually either by an attraction of Newton's law of gravitation or by an electrostatic repulsion of Coulomb's law, under a background downward gravity in a horizontally-periodic 3D half-space, whose inflow distribution at the boundary is prescribed. We investigate a nonlinear asymptotic stability of its generic steady states in the dynamical kinetic PDE theory of the Vlasov-Poisson equations. We construct Lipschitz continuous space-inhomogeneous steady states and establish exponentially fast asymptotic stability of these steady states with respect to small perturbation in a weighted Sobolev topology. In this proof, we crucially use the Lipschitz continuity in the velocity of the steady states. Moreover, we establish well-posedness and regularity estimates for both steady and dynamic problems.
