BILINEAR STRICHARTZ ESTIMATESFOR SCHRODINGER OPERATORSIN TWO-DIMENSIONAL COMPACT MANIFOLDSWITH BOUNDARY AND CUBIC NLS

摘要

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