Strong attractors for weakly damped quintic wave equation in bounded domains

Abstract

In this paper, we study the longtime dynamics for the weakly damped wave equation with quintic non-linearity in a bounded smooth domain of ${\mathbb{R}}^3.$ Based on the Strichartz estimates for the case of bounded domains, we establish the existence of a strong global attractor in the phase space $H^2(\Omega )\cap H_0^1(\Omega )\times H_0^1(\Omega )$. Moreover, the finite fractal dimension of the attractor is also shown with the help of the quasi-stable estimation.

18 pages