Talk Abstracts

We consider the Cauchy problem for the derivative fractional nonlinear Schrodinger (fNLS) on the torus. In this talk, we give a necessary and sufficient condition on the nonlinearity for well-posedness. For semi-linear Schrodinger equations, a gauge transformation is effective in canceling the worst part of the nonlinear interaction. However, since we can not employ a gauge transformation for derivative fNLS, we instead use the modified energy method to prove well-posedness. In particular, we need to inductively construct correction terms for the modified energy when the order of the fractional Laplacian lies between 1 and 3/2 . This talk is based on a joint work with Takamori Kato (Saga University) and Toshiki Kondo (The University of Osaka).