Global axisymmetric Euler flow with rotation

Rotation (e.g. Coriolis force) plays an important role in the dynamics of large scale fluid dynamics modeled by incompressible Euler equations. Thanks to decay and dispersive effect from a constant rotation, we establish asymptotic stability smooth axisymmetric incompressible Euler flows in the presence of a constant rotation force with a non-trivial swirl. We will review the recent progress on dispersive effects and global stability for nonlinear PDE, particularly in the framework of control of space-time resonance.