中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：张 伟 博士后 （首都师范大学）
题 目：On the Finite-Time Splash for the free boundary incompressible Navier–Stokes equations (I)
时 间：2023.05.16（星期二）13:30-16:00
地 点：数学院南楼N802
摘 要：In this talk, we consider the incompressible Navier-Stokes equations with free boundary, which has a finite-time splash singularity for a large class of specially prepared initial data. The approach is founded upon the Lagrangian description of the free-boundary problem, and a sequence of domains Ωε used as the initial data for the splash singularity are defined, wherein the boundary Γε of these domains is close to self-intersection between two approaching portions of Γε. We will present some preliminary lemmas which show that the constant appearing in elliptic estimates and the Sobolev embedding theorem is independent of ε and define the sequence of initial divergence-free velocity fields that are guaranteed to satisfy the required single compatibility condition, and whose norm is independent of ε.
