Colloquium| Institute of Mathematical Sciences
Time：14:00-15:00, Tursday, December 26
Location：Room S408, IMS
Speaker: Haitian Yue
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 (08â€™), 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.