Bilinear Strichartz estimates for Schr\"odinger operators in 2 dimensional compact manifolds with boundary and cubic NLS
Abstract
In this paper, we establish bilinear and gradient bilinear Strichartz estimates for Schr\"odinger operators in 2 dimensional compact manifolds with boundary. Using these estimates, we can infer the local well-posedness of cubic nonlinear Schr\"odinger equation in Hs for every s>2/3 on such manifolds.
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