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 we discuss with some context. In our approach, it is captured in a « method of partial symmetries », which 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).