APDE Seminar@UPV/EHU : Existence and regularity results for the sub-Riemannian Navier-Stokes system

In this talk, I will introduce a new class of models called sub-Riemannian Navier-Stokes systems that model an incompressible fluid whose velocity field admits an anisotropy resulting from a geometric structure. We show the global existence of finite energy (weak) solutions for any initial data belonging to $L^2$. Then, we will establish the well-posedness in a suitable Sobolev-type critical space that takes into account the structure of the system and the underlying geometry. Finally, I will describe the smoothing effects through which we found the anisotropic structure of the equations.

The analysis strongly involves the sub-Riemannian geometric structure of stratified Lie groups and tools from non-commutative harmonic analysis.