Modul: MAT675 PDE and Mathematical Physics

## Global axisymmetric Euler flows with rotation

Talk by Prof. Dr. Klaus Widmayer

**Date:** 10.03.22 **Time:** 16.00 - 17.00 **Room:** ETH HG G 19.1

We discuss the construction of a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform "rigid body" rotation. These solutions are axisymmetric, of Sobolev regularity and have non-vanishing swirl. At the heart of this result is a dispersive effect due to rotation, which is captured in our "method of partial symmetries". This approach is adapted to maximally exploit the symmetries of this anisotropic problem, both for the linear and nonlinear analysis, and allows to globally propagate sharp decay estimates. This is joint work with Y. Guo and B. Pausader (Brown University).