Banach空间中零粘性随机Boussinesq方程的不变测度

Pub Date : 2022-10-16 DOI:10.1080/14689367.2022.2128991

Shang Wu, Zhiming Liu, Jianhua Huang

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引用次数: 0

摘要

本文研究了二维域上高斯噪声驱动的随机Boussinesq方程。通过对高阶Sobolev空间的正则性估计，证明了不可分Banach空间弱解的存在性。我们还证明了由随机Boussinesq方程解生成的马尔可夫半群也是弱Feller。与弱者同在-★ 拓扑上，我们用Krylov–Bogoliubov定理证明了不变测度的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Invariant measure of stochastic Boussinesq equation with zero viscosity in Banach space

In this paper, we investigate the stochastic Boussinesq equations driven by Gaussian noise on a two-dimensional domain . By the regularity estimation on the high-order Sobolev space, we prove the existence of weak solutions in non-separable Banach space. We also show that the Markov semigroup generated by the solution of stochastic Boussinesq equations is also weak Feller. Endowed with the weak-★ topology on , we prove the existence of the invariant measure by Krylov–Bogoliubov theorem.

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