Invariant measures for stochastic Burgers equation on unbounded domains

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Hauptverfasser: Liu, Zhenxin, Shi, Zhiyuan
Format: Preprint
Veröffentlicht: 2025
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author Liu, Zhenxin
Shi, Zhiyuan
author_facet Liu, Zhenxin
Shi, Zhiyuan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_07119
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Invariant measures for stochastic Burgers equation on unbounded domains
Liu, Zhenxin
Shi, Zhiyuan
Dynamical Systems
Probability
35Q35, 35R60, 60H15
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.
title Invariant measures for stochastic Burgers equation on unbounded domains
topic Dynamical Systems
Probability
35Q35, 35R60, 60H15
url https://arxiv.org/abs/2506.07119