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

Abstract

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