论文标题
2D Navier-Stokes方程与随机相互作用粒子系统产生涡度的均匀近似
Uniform Approximation of 2D Navier-Stokes Equations with Vorticity Creation by Stochastic Interacting Particle Systems
论文作者
论文摘要
我们考虑一个具有反射边界的有界域中的随机相互作用粒子系统，包括在给定源项规定的边界上创建新粒子。我们表明，这种粒子系统以涡度形式和不可渗透的边界近似于2D Navier-Stokes方程，这是在边界处建模涡度创建的粒子的创建。内核平滑，更具体地说，通过空间域上的neumann热半群来平滑，可以使正则经验措施均匀地收敛到（弱解决）Navier-Stokes方程。
We consider a stochastic interacting particle system in a bounded domain with reflecting boundary, including creation of new particles on the boundary prescribed by a given source term. We show that such particle system approximates 2d Navier-Stokes equations in vorticity form and impermeable boundary, the creation of particles modeling vorticity creation at the boundary. Kernel smoothing, more specifically smoothing by means of the Neumann heat semigroup on the space domain, allows to establish uniform convergence of regularized empirical measures to (weak solutions of) Navier-Stokes equations.
