Infinite energy solutions for weakly damped quintic wave equations in $\mathbb{R}^3$
Analysis of PDEs
2020-04-27 v1
Abstract
The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in 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.
Keywords
Cite
@article{arxiv.2004.11864,
title = {Infinite energy solutions for weakly damped quintic wave equations in $\mathbb{R}^3$},
author = {Xinyu Mei and Anton Savostianov and Chunyou Sun and Sergey Zelik},
journal= {arXiv preprint arXiv:2004.11864},
year = {2020}
}