Strichartz estimates for the fractional Schrödinger and wave equations on compact manifolds without boundary

Abstract

We firstly prove Strichartz estimates for the fractional Schrödinger equations on Rd,d≥1 endowed with a smooth bounded metric g. We then prove Strichartz estimates for the fractional Schrödinger and wave equations on compact Riemannian manifolds without boundary (M,g). This result extends the well-known Strichartz estimate for the Schrödinger equation given in [1]. We finally give applications of Strichartz estimates for the local well-posedness of the pure power-type nonlinear fractional Schrödinger and wave equations posed on (M,g).