CMSA Interdisciplinary Science Seminar: Weak solutions to the isentropic system of gas dynamics
Cheng Yu - Department of Mathematics, University of Florida
In this talk, I will discuss the global weak solutions to the isentropic system of gas dynamics: existence and non-uniqueness. In the first part, we generalized the renormalized techniques introduced by DiPerna-Lions to build up the global weak solutions to the compressible Navier-Stokes equations with degenerate viscosities. This existence result holds for any $\gamma>1$ in any dimensional spaces for the large initial data. In the second part, we proved that for any initial data belonging to a dense subset of the energy space, there exists infinitely many global weak solutions to the isentropic Euler equations for any $1<\gamma\leq 1+2/n$. Our result is based on a generalization of convex integration techniques by De Lellis-Szekelyhidi and weak vanishing viscosity limit of the Navier-Stokes equations. The first part is based on the joint works with D. Bresch and A. Vasseur, and the second one is based on our recent joint work with R. M Chen and A. Vasseur.