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: 本文研究了在所有方向具有慢扩散的条件下带延迟的随机异向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,我们给出了相应的异向Navier-Stokes方程平稳解的存在唯一性。在此基础上,我们继续研究了弱解的指数稳定性。我们的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 sufficient to guarantee the existence, uniqueness and exponential stability of stationary solutions. This is new even for stochastic anisotropic Navier-Stokes equations without delay.

     

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