Strichartz estimates for the fractional Schr\"odinger and wave equations   on compact manifolds without boundary
  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 $(M,g)$. 
Van Duong Dinh
math.AP