Low-regularity well-posedness for the derivative nonlinear Schrödinger equation

2018/02/09 Fri 15:30 - 16:30
Room 251, Building No.3
Razvan Mosincat
The University of Edinburgh

In this talk, we first consider the derivative nonlinear Schrödinger equation (DNLS) on the torus. By employing the Fourier restriction norm method, the $I$-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao, the normal form method, and a coercivity property in the spirit of Guo and Wu, we prove global well-posedness in $H^{1/2}(\mathbb{T})$, provided initial data with mass less than $4\pi$.  Then, we consider DNLS on the real-line and study the uniqueness of its solutions. In particular, by implementing an infinite iteration of the normal form reductions based on a scheme introduced by Guo, Kwon, and Oh, we prove unconditional uniqueness for DNLS in $H^s(\mathbb{R})$, $s>1/2$. The second part is joint work with Haewon Yoon (Korea Advanced Institute of Science and Technology).