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： Dr. Kexin Jin (Princeton university and Tsinghua university)
题 目：Long time dynamics of the NLS
时 间：2021.12.06（星期一），10:00-11:00
地 点：数学院南楼N210室
摘 要：We prove a vanishing property of the normal form transformation of the 1D cubic nonlinear Schr\"odinger (NLS) equation with periodic boundary conditions on $[0,L]$. We apply this property to quintic resonance interactions and obtain a description of dynamics for time up to $T=\frac{L^2}{\epsilon^4}$, if $L$ is sufficiently large and size of initial data $\epsilon$ is small enough. Since $T$ is the characteristic time of wave turbulence, this result implies the absence of wave turbulence behavior of 1D cubic NLS. Joint with Xiao Ma.
报告人简介：Kexin Jin is PhD student in Princeton university under supervision of Alex Ionescu and Tristan Buckmaster. In this semester, she is visiting Tsinghua university. She is interested in long time dynamics of partial differential equations on fluid mechanics and nonlinear dispersive equations. She is also interested in applying PDE theory to theoretical machine learning.
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