带延迟的随机异向Navier-Stokes模型的渐近行为

The Asymptotic Behavior of Stochastic Anisotropic Navier-Stokes Models with Delays

  • 摘要: 本文在所有方向具有慢扩散的条件下,研究了带延迟的随机异向Navier-Stokes方程弱解的轨道指数稳定性.借助于异向Sobolev空间嵌入定理,给出了相应的异向Navier-Stokes方程平稳解的存在唯一性.在此基础上,研究了弱解的指数稳定性.本文主要结果提供了生长指数之间的一种关系,这种关系足以保证平稳解的存在唯一性和指数稳定性.这一工作对于无延迟的随机异向Navier-Stokes方程也是新的.

     

    Abstract: The aim of this work is to study the pathwise exponential stability of weak solutions of stochastic anisotropic Navier-Stokes equations with delays under the assumptions of slow diffusion in all directions. The existence and uniqueness of stationary solutions to the associated anisotropic Navier-Stokes equations are shown by using the embedding of anisotropic Sobolev spaces. Based on this conclusion, we continue to explore the exponential stability of weak solutions. Our main result provides a relationship among the growth exponents that is suffcient to guarantee the existence, uniqueness and exponential stability of stationary solutions. This is new even for stochastic anisotropic Navier-Stokes equations without delay.

     

/

返回文章
返回