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.