中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：廖娴（KIT）
题 目：Conserved energies for the one-dimensional Gross-Pitaevskii equation
时 间：2022.10.11（星期二）16:00-17:00
地 点：腾讯会议：186 715 161
摘 要：In this talk we will consider the Cauchy problem for the one-dimensional Gross-Pitaevskii equation, which is a defocusing cubic nonlinear Schrödinger equation but under nonzero boundary conditions at infinity. We will first introduce our (generalized) energy space, and study its analytical and topological structures. We will then define the (renormalized) transmission coefficient associated to the Lax operator of the Gross-Pitaevskii equation on this energy space, and construct a family of conserved energies, which will imply the global-in-time well-posedness result. This is joint work with Herbert Koch (Bonn, Germany).
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