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

[摘要] We firstly prove Strichartz estimates for the fractional Schrodinger equations on R-d, d >= 1 endowed with a smooth bounded metric g. We then prove Strichartz estimates for the fractional Schrodinger and wave equations on compact Riemannian manifolds without boundary (M, g). This result extends the well-known Strichartz estimate for the Schrodinger equation given in [1]. We finally give applications of Strichartz estimates for the local well-posedness of the pure power-type nonlinear fractional Schrodinger and wave equations posed on (M, g). (C) 2017 Elsevier Inc. All rights reserved.

[发布日期] 2017-12-15

[关键词] Nonlinear fractional Schrodinger equation;Strichartz estimates;WKB approximation;Pseudo-differential calculus