Infinite energy solutions for weakly damped quintic wave equations in ℝ³

2020/04/24 by Xinyu Mei, Anton Savostianov, Mei, Xinyu +5
Engineering · Mathematics · #35B40 #35B45 #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.11864

openalex publication_date 2020/04/24 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28

Abstract

The paper gives a comprehensive study of infinite-energy solutions and their long-time behavior for semi-linear weakly damped wave equations in ℝ³ 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.

Citations

• Uniform attractors for measure-driven quintic wave equation with\n periodic boundary conditions

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• Attractors for damped quintic wave equations in bounded domains