Infinite energy solutions for weakly damped quintic wave equations in ${\mathbb{R}}^3$

Abstract

The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in ${\mathbb{R}}^3$ with quintic nonlinearities. This study includes global well-posedness of the so-called Shatah-Struwe solutions, their dissipativity, the existence of a locally compact global attractors (in the uniformly local phase spaces) and their extra regularity.

References in corpus (1)

• Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains

Cited by in corpus (1)

• Asymptotic regularity and attractors for slightly compressible Brinkman-Forcheimer equations