中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

报告人：Prof. Nicolas Burq (University of Paris-Sud)

题  目：Almost sure global existence and scattering for the one dimensional non linear Schrodinger equation

时  间：2018.06.07（星期四）, 16:20-17:20

地  点：数学院南楼N913室

摘  要：

We consider the one-dimensional nonlinear Schr？dinger equation with a nonlinearity of degree 1<p. The purpose of this talk is twofold. First we exhibit measures on the space of initial data $H^s(\mathbb{R})$ s<0, for which we can describe the (non trivial) evolution by the linear Schr？dinger flow (recall that on $\mathbb{R}^n$, there are no (non trivial) measures invariant by the linear flow). Then we define an almost sure flow and we show that the evolution of these mesaures by the non linear flow is absolutely continuous with respect to evolution by the linear flow. We actually give{\em quantitative} versions of this absolute continuity. We deduce from this precise description the global well-posedness for p>1and scattering for p>3.