Joint CMU-Pitt Colloquium: Global solutions to the compressible Navier-Stokes equation with degenerate viscosity coefficients

Friday, February 9, 2018 - 16:00
Thackeray Hall 704
Speaker Information
Alexis Vasseur
University of Texas at Austin

Abstract or Additional Information

Joint CMU-Pitt Colloquium

4pm, Friday, February 9

Thackeray Hall 704

Reception Immediately Following the Colloquium


Title: Global solutions to the compressible Navier-Stokes equation with degenerate viscosity coefficients

Abstract: We prove the existence of global weak solutions for 2D and 3D compressible
Navier-Stokes equations with degenerate viscosities. Those models include
the viscous shallow water equations.  The method is based on the Bresch
and Desjardins entropy. The main contribution is to derive the
Mellet-Vasseur type inequality for the weak solutions, even if it is not
verified by the first level of approximation. This provides existence of
global solutions in time, for the barotropic compressible Navier-Stokes
equations, in three dimensional space, with large initial data, possibly
vanishing on the vacuum. This is a joint work with Cheng Yu published in
Inventiones Mathematicae.