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arXiv · 1104.0447

Global Well-posedness of the Stochastic Kuramoto-Sivashinsky Equation with Multiplicative Noise

Wei Wu·Shangbin Cui·Jinqiao Duan
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Abstract

Global well-posedness of the initial-boundary value problem for the stochastic Kuramoto-Sivashinsky equation in a bounded domain $D$ with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any initial data $u_0\in L^2(D\times \Omega)$ this problem has a unique global solution $u$ in the space $L^2(\Omega,C([0,T],L^2({D})))$ for any $T>0$, and the solution map $u_0\mapsto u$ is Lipschitz continuous.

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Wei Wu, Shangbin Cui, Jinqiao Duan. 2011-04-04. Global Well-posedness of the Stochastic Kuramoto-Sivashinsky Equation with Multiplicative Noise. https://arxiv.org/abs/1104.0447

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