Séminaire Analyse non linéaire et EDP

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 […]