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

van Duong Dinh (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 $(M, g)$.

Mots clés: Nonlinear fractional Schrödinger equation; Strichartz estimates; WKB approximation; Pseudo-differential calculus

Domaines: Equations aux dérivées partielles [math.AP]

van Duong Dinh. Strichartz estimates for the fractional Schrödinger and wave equations on compact manifolds without boundary. Journal of Differential Equations, 2017, 263 (12), pp.8804-8837. ⟨hal-01426760v2⟩