IMPROVED STRICHARTZ ESTIMATES FOR A CLASS OF DISPERSIVE EQUATIONS IN THE RADIAL CASE AND THEIR APPLICATIONS TO NONLINEAR SCHR?DINGER AND WAVE EQUATIONS

摘要

We prove some new Strichartz estimates for a class of dispersive equations with radial initial data. In particular, we obtain the full radial Strichartz estimates up to some endpoints for the Schr?dinger equation. Using these estimates, we obtain some new results related to nonlinear problems, including small data scattering and large data LWP for the nonlinear Schr?dinger and wave equations with radial critical initial data and the well-posedness theory for the fractional order Schr?dinger equation in the radial case.