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：W. S. Ożański (Florida State University)
题 目：Linear and nonlinear instability of 3D vortex columns
时 间：2023.12.04（星期一）09:00-10:00
地 点：Zoom ID: 924 888 5804 Passcode: AMSS2022
摘 要：We will discuss stability properties of steady solutions to the 3D incompressible Euler equations in the form of vortex columns, u = V (r)eθ + W (r)ez, for a family of profiles V, W . We will discuss a construction of countably many linearly unstable modes, which are not of neutral limiting type, but instead they exhibit a multiscale behaviour which can be captured using a new functional framework of Lyapunov-Schmidt reduction and gluing procedure. The modes are of the form of “ring modes” that are localized near some r0 (in cylindrical coordinates). We will also discuss how each of these ring modes gives rise to nonlinear instability. This is joint work with D. Albritton.
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