Minimal regularity solutions of nonlinear wave equations
type: Item
instance of: scholarly article
title: Minimal regularity solutions of nonlinear wave equations
zbMATH Open document ID: 0896.35084
author: Hans Lindblad
published in: Documenta Mathematica
publication date: 1998-08-05T00:00:00Z
full work available at URL: https://eudml.org/doc/227314
full work available at URL: Lindblad.MAN.html
review text: Summary: Inspired by the need to understand the complex systems of non-linear wave equations which arise in physics, there has recently been much interest in proving existence and uniqueness for solutions of nonlinear wave equations with low regularity initial data. We give counterexamples to local existence with low regularity data for the typical nonlinear wave equations. In the semi-linear case these are sharp, in the sense that with slightly more regularity one can prove local existence. We also present join work with Georgiev and Sogge proving global existence for a certain class of semi-linear wave equation. This result was a conjecture of Strauss following an initial result of Fritz John. We develop weighted Strichartz estimates whose proof uses techniques from harmonic analysis taking into account the symmetries of the wave equation.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B65
zbMATH DE Number: 1184344
zbMATH Keywords: low regularity initial data
zbMATH Keywords: counterexamples to local existence
zbMATH Keywords: weighted Strichartz estimates
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1184344