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

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Dynamical Systems-An International Journal Pub Date : 2022-10-16 DOI:10.1080/14689367.2022.2128991

Shang Wu, Zhiming Liu, Jianhua Huang

引用次数: 0

Abstract

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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Banach空间中零粘性随机Boussinesq方程的不变测度

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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来源期刊

Dynamical Systems-An International Journal 物理-力学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Dynamical Systems: An International Journal is a world-leading journal acting as a forum for communication across all branches of modern dynamical systems, and especially as a platform to facilitate interaction between theory and applications. This journal publishes high quality research articles in the theory and applications of dynamical systems, especially (but not exclusively) nonlinear systems. Advances in the following topics are addressed by the journal: •Differential equations •Bifurcation theory •Hamiltonian and Lagrangian dynamics •Hyperbolic dynamics •Ergodic theory •Topological and smooth dynamics •Random dynamical systems •Applications in technology, engineering and natural and life sciences