报告题目：On the Nonlinear Schrödinger Equation with Derivative

报告时间：2021-12-06  15:00-17:00

报告人：Prof. Hajer Bahouri (法国索邦大学)

ZOOMID：844 4970 8290    密码：20211206

报告链接：https://zoom.us/j/84449708290?pwd=Y1hWQmdVNUZZeVlKZHhYRnNaR1hoQT09

Abstract: This lecture is dedicated to the study of the derivative nonlinear Schrödinger equation (DNLS) on the real line, The DNLS equation was introduced by Mio-Ogino-Minami-Takeda and Mjolhus, and it has received a great deal of attention from the mathematics community after being shown to be completely integrable by Kaup-Newell. The local well-posedness of this equation in the Sobolev spaces Hs (R) is well understood since a couple of decades.

　In this lecture, we shall focus on the issue of global well-posedness: we will mainly be interested by the result of Bahouri-Perelman where the authors prove that the (DNLS) equation is globally well-posed for general Cauchy data in H(1/2) (R) and that furthermore the H(1/2) norm of the solutions remains globally bounded in time. The proof is achieved by combining the profile decomposition techniques with the integrability structure of the equation.