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

2015/11/14 by Anton Savostianov, Savostianov, Anton
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 #math.AP #msc:35B40 #msc:35B45 #msc:35L70

paper · pdf · doi:10.48550/arxiv.1511.04592

arxiv created 2015/11/14 · openalex publication_date 2015/11/14 · arxiv updated 2015/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 (-Δ_x+1)^(1)/(2)∂_t u. 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.

Related

• Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains
• Infinite energy solutions for weakly damped quintic wave equations in ℝ³
• Smooth attractors for the quintic wave equations with fractional damping
• Attractors for damped quintic wave equations in bounded domains
• On global existence for semilinear wave equations with spacedependent critical damping