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arXiv · 0909.2902

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

Jin-Cheng Jiang
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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.

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Jin-Cheng Jiang. 2009-09-16. Bilinear Strichartz estimates for Schrödinger operators in 2 dimensional compact manifolds with boundary and cubic NLS. https://arxiv.org/abs/0909.2902

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