JournalsrmiVol. 25, No. 2pp. 693–708

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

  • Kunio Hidano

    Mie University, Mie-Ken, Tsu-Shi, Japan
Small solutions to semi-linear wave equations with radial data of critical regularity cover
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Abstract

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 L2L^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.

Cite this article

Kunio Hidano, Small solutions to semi-linear wave equations with radial data of critical regularity. Rev. Mat. Iberoam. 25 (2009), no. 2, pp. 693–708

DOI 10.4171/RMI/579