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Jin-Cheng Jiang

2009-12-17
15:30:00 - 16:30:00

Bilinear Strichartz estimates for Schr\"{o}dinger operators in 2 dimensional compact manifolds with boundary

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk, we will talk about the bilinear Strichartz estimates for Schr\"{o}dinger operators in 2 dimensional compact manifolds with boundary. Using these estimates, we can infer the local well-posedness of cubic nonlinear Schr\"{o}dinger equation in $H^s$ for every $s>\frac{2}{3}$ on such manifolds by standard nonlinear analysis. Hence we will focus on the ideas of building such estimates in compact manifolds.