Title：Optimal Local well-posedness for the periodic derivative nonlinear Schrodinger equation
Time：2019年12月23日 上午 09:00-10:00
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.