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 $\mathbb{R}^d , d \geq 1$ 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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Strichartz Fractional Schrodinger Compact Manifolds.pdf (501.48 Ko)
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