标题： 随机Burgers方程在无界域上的不变测度 显示英文标题

标题： Invariant measures for stochastic Burgers equation on unbounded domains

摘要： 本文研究了在整个实线上定义的带乘性噪声的随机阻尼Burgers方程。 我们证明了该随机阻尼Burgers方程温和解的存在性和唯一性，并建立了解在时间上一致有界的性质。 此外，通过利用解的尾部的一致估计，我们得到了解的概率分布族的紧性。 随后，通过应用Krylov-Bogoliubov定理，我们建立了不变测度的存在性。 显示英文摘要

摘要： In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and establish that the solution is uniformly bounded in time. Furthermore, by employing the uniform estimates on the tails of the solution, we obtain the tightness of a family of probability distributions of the solution. Subsequently, by applying the Krylov-Bogolioubov theorem, we establish the existence of invariant measures.