We consider the three dimensional (incompressible) Euler-Coriolis system for axisymmetric velocity fields. Using dispersive analysis, we prove that small and localized initial data lead to solutions which exist for a large time ($\varepsilon^{-M}$). The speed of rotation is fixed and our initial data can have swirl.

The proof combines a careful analysis of the null structure of the equation, the degenerate dispersive properties of the linearized flow and various bilinear estimates. This is a joint work with Y. Guo and K. Widmayer.