Local Existence for Nonlinear Wave Equation with Radial Data in 2+1 Dimensions

Abstract

We get a local existence result in $H^s$ with $s>3/2$ for second order quasilinear wave equation with radial initial data in 2+1 dimensions, based on an improvement of Strichartz estimate in the radial case. Moreover, we get the corresponding local well-posed result for semilinear wave equation. The required index of regularity here is 1/4 less than the index 7/4, which is essentially sharp in general.

19pages, no figures

References in corpus (1)

• Some Remarks on Strichartz Estimates for Homogeneous Wave Equation