Random attractors of supercritical wave equations driven by infinite-dimensional additive noise on $ \mathbb{R}^n $

Abstract

<p style='text-indent:20px;'>In this paper, we prove the existence and uniqueness of tempered pullback random attractors of the supercritical stochastic wave equations driven by an infinite-dimensional additive white noise on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula> with <inline-formula><tex-math id="M3">\begin{document}$ n\le 6 $\end{document}</tex-math></inline-formula>. We first construct a tempered pullback random absorbing set in the natural energy space, and then establish the pullback asymptotic compactness of the solution operator by applying the idea of uniform tail-ends estimates as well as the uniform Strichartz estimates of solutions to circumvent the lack of compactness of Sobolev embeddings on unbounded domains.</p>