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 ${\mathbb{R}}^d$ 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 $(M,g)$. 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 $(M,g)$.

Revised Version

References in corpus (2)

• Physical interpretation of fractional diffusion-wave equation via lossy media obeying frequency power law
• Well-posedness of nolinear fractional Schrödinger and wave equations in Sobolev spaces

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