Small solutions to semi-linear wave equations with radial data of critical regularity
type: Item
instance of: scholarly article
title: Small solutions to semi-linear wave equations with radial data of critical regularity
zbMATH Open document ID: 1181.35147
DOI: 10.4171/RMI/579
author: Kunio Hidano
published in: Revista Matemática Iberoamericana
publication date: 2009-10-13T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1255440071
full work available at URL: https://eudml.org/doc/43576
review text: Summary: This paper investigates the problem of global existence of small solutions to semi-linear wave equations with radially symmetric data of critical regularity. Under radial symmetry, we focus on the case where the power of nonlinear term is somewhat smaller than the conformal power. Our result covers the case where the power is strictly larger than the John-Glassey exponent in two or three space dimensions. In higher dimension it applies to the equation whose power is strictly larger than the \(L^2\)-critical exponent. The main theorem is therefore an improvement over a previous result due to Lindblad and Sogge. The new ingredient in our proof is an effective use of some weighted estimates of radially symmetric solutions to inhomogeneous wave equations.
Mathematics Subject Classification ID: 35L71
Mathematics Subject Classification ID: 35L15
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 5614589
zbMATH Keywords: low-regularity solution
zbMATH Keywords: weighted estimate
zbMATH Keywords: John-Glassey exponent
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5614589