Strichartz estimates for the fractional Schrödinger and wave equations on compact manifolds without boundary
Résumé
We firstly prove Strichartz estimates for the fractional Schrödinger equations on R d , 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 [7]. 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).
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