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arXiv · 1609.07305

Strichartz estimates for the fractional Schr\"odinger and wave equations on compact manifolds without boundary

Van Duong Dinh
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Abstract

We firstly prove Strichartz estimates for the fractional Schr\"odinger equations on $\mathbb{R}^d$ endowed with a smooth bounded metric $g$. We then prove Strichartz estimates for the fractional Schr\"odinger 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 Schr\"odinger and wave equations posed on $(M,g)$.

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Van Duong Dinh. 2016-09-23. Strichartz estimates for the fractional Schr\"odinger and wave equations on compact manifolds without boundary. https://doi.org/10.1016/j.jde.2017.08.045

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