On global regularity for systems of nonlinear wave equations with the null-condition
type: Item
instance of: scholarly article
title: On global regularity for systems of nonlinear wave equations with the null-condition
zbMATH Open document ID: 1336.35242
author: Aparajita Dasgupta
author: Can Gao
author: Joachim Krieger
published in: Dynamics of Partial Differential Equations
publication date: 2015-10-08T00:00:00Z
review text: In this note the authors investigate the problem of global regularity for systems of semilinear wave equations on Minkowski space \(\mathbb R^{3+1}\), satisfying null condition. It has been well known that the problem admit global solutions provided the initial data is compactly supported and sufficiently small and smooth. The main result in this note is the pointwise decay for solutions of the form \(| u|\leq C (1+| t-| x\|)^{-1}(1+t+| x|)^{-1}\), by assuming small bound on \(\| (1+| x|)^{2s-1}(u(0),\partial u(0))\|_{H^s\times H^{s-1}}\) (\(s>3/2\) which is almost optimal concerning on the regularity) for compactly supported initial data.
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 6491693
zbMATH Keywords: well-posedness
zbMATH Keywords: Penrose compactification
zbMATH Keywords: null condition
reviewed by: Chengbo Wang
MaRDI profile type: Publication
DOI: 10.4310/DPDE.2015.V12.N2.A2
description: scientific article; zbMATH DE number 6491693