Bilinear Strichartz estimates for Schrödinger operators in 2 dimensional compact manifolds with boundary and cubic NLS

Abstract

In this paper, we establish bilinear and gradient bilinear Strichartz estimates for Schrödinger operators in 2 dimensional compact manifolds with boundary. Using these estimates, we can infer the local well-posedness of cubic nonlinear Schrödinger equation in $H^s$ for every $s>2/3$ on such manifolds.

22 pages