Logo

Mathematical Sciences Research Institute

Home » Workshop » Schedules » Arnold's variational principle and its application to the stability of viscous planar vortices

Arnold's variational principle and its application to the stability of viscous planar vortices

[Moved Online] Recent Developments in Fluid Dynamics April 12, 2021 - April 30, 2021

April 13, 2021 (08:00 AM PDT - 08:50 AM PDT)
Speaker(s): Thierry Gallay (Université Grenoble Alpes (Université de Grenoble I - Joseph Fourier))
Location: MSRI: Online/Virtual
Tags/Keywords
  • Two-dimensional vortices

  • stability

  • variational techniques

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video
No Video Uploaded
Abstract

We revisit the variational approach to nonlinear stability of planar flows, which was developed by V. I. Arnold around 1965. In particular, we study the coercivity properties of the quadratic form that describes the second variation of the energy at a radially symmetric vortex with strictly decreasing vorticity profile. We also show that this quadratic form can be used to obtain a new proof of nonlinear stability for the Lamb-Oseen vortices, which are self-similar solutions of the two-dimensional Navier-Stokes equations. This is all joint work with Vladimir Sverak.

Supplements No Notes/Supplements Uploaded
Video/Audio Files
No Video Files Uploaded