Klaus Widmayer

We investigate long time dynamics of solutions to the rotating Euler equations in three spatial dimensions. We develop a framework that is adapted to the symmetries and the dispersive properties of this problem and show how it can be used to understand the behavior of small data solutions, uniformly in the parameter of rotation.

The key idea is to use the available symmetries as much as possible, rather than to pursue a more brute force approach. While this streamlines the deduction of some energy type estimates, it also requires a fresh look at the (linear) dispersive estimates, deviating from the classical stationary phase intuition.