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

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

2007-05-20

arxiv.org/abs/0705.2849v1

Mathematics

Analysis of PDEs

19pages, no figures

Scientific paper

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.

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