Revista Matemática Iberoamericana


Full-Text PDF (215 KB) | Metadata | Table of Contents | RMI summary
Volume 25, Issue 2, 2009, pp. 693–708
DOI: 10.4171/RMI/579

Published online: 2009-08-31

Small solutions to semi-linear wave equations with radial data of critical regularity

Kunio Hidano[1]

(1) Mie University, Mie-Ken, Tsu-Shi, Japan

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.

Keywords: Wave equation, low-regularity solution, weighted estimate

Hidano Kunio: Small solutions to semi-linear wave equations with radial data of critical regularity. Rev. Mat. Iberoamericana 25 (2009), 693-708. doi: 10.4171/RMI/579