Well-posedness for viscous compressible fluids with only bounded density

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}.

Date: Mar 11, 2019 at 16:00:00 h
Venue: Sala John Von Neumann del CMM, séptimo piso CMM, Torre Norte de Beauchef 851.
Speaker: Francesco Fanelli
Affiliation: Institut Camille Jordan, Lyon-1, Francia
Coordinator: Matteo Rizzi
Abstract:
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Posted on Mar 6, 2019 in CAPDE, Seminars