Infinite energy solutions for critical wave equation with fractional damping in unbounded domains

Abstract

This work is devoted to infinite-energy solutions of semi-linear wave equations in unbounded smooth domains of R3 with fractional damping of the form (−Δx+1)12∂tu. The work extends previously known results for bounded domains in finite energy case. Furthermore, well-posedness and existence of locally-compact smooth attractors for the critical quintic non-linearity are obtained under less restrictive assumptions on non-linearity, relaxing some artificial technical conditions used before. This is achieved by virtue of new type Lyapunov functional that allows to establish extra space–time regularity of solutions of Strichartz type.