数学科学研究所
Insitute of Mathematical Science

Colloquium:Optimal local well-posedness for the periodic derivative nonlinear Schrodinger equation

Colloquium| Institute of Mathematical Sciences

Time14:00-15:00, Tursday, December 26

LocationRoom S408, IMS

 

Speaker:  Haitian Yue

AbstractIn 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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