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

We get a local existence result in $H^s$ with $s>3\mathrm{/}2$ 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.