12-23【岳海天】管楼1418 吴文俊数学重点实验室微分方程系列报告

时间:2019-12-23


Title:Optimal Local well-posedness for the periodic derivative nonlinear Schrodinger equation

Speaker:岳海天   (南加州大学)

Time:2019年12月23日         上午    09:00-10:00

Room:东区管理科研楼  1418室


Abstract:In this talk, we consider the periodic derivative nonlinear Schrodinger's equation, which is L^2 critical. We show local well-posedness in Fourier-Lebesgue spaces which scale like H^s(T) for s>0. In particular we close the existing gap in the subcritical theory by improving the result of Grunrock-Herr (08), which established local well-posedness in Fourier-Lebesgue spaces which scale like H^s(T) for s>1/4. We achieve this result by a delicate analysis of the structure of the solution and the construction of an adapted nonlinear submanifold of a suitable function space.


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