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.
Citation
Jin-Cheng Jiang. "Bilinear Strichartz estimates for Schrödinger operators in two-dimensional compact manifolds with boundary and cubic NLS." Differential Integral Equations 24 (1/2) 83 - 108, January/February 2011. https://doi.org/10.57262/die/1356019046
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