Abstract:
In this talk, we consider the well-posedness issue for the barotropic Navier-Stokes equations. We consider initial velocity fields which have (slightly) sub-critical regularity, and initial densities which are (essentially) only bounded; in particular, we can consider densities having discontinuities across an interface. We are able to establish a local in time existence and uniqueness result in any space dimension, generalising previous results due to Hoff.
The proof combines a maximal regularity approach with the study of propagation of geometric structures, in the same spirit of striated regularity \textsl{\`a la Chemin}.