Special Session 31: Variational energy and entropy approaches in non-smooth thermomechanics
Contents
In this talk we discuss the well-posedness problem for weak solutions of the compressible isentropic Euler system in $2$ space dimensions with particular attention to the role of the maximal dissipation criterion proposed by Dafermos.
The results we present in collaboration with C. De Lellis and O. Kreml are in the line with the program of investigating the efficiency of different selection criteria proposed in the literature in order to weed out non-physical solutions to more-dimensional systems of conservation laws.
Specifically we will illustrate how some non-standard (i.e. constructed via convex integration methods) solutions to the Riemann problem for the isentropic Euler system in $2$ space dimensions have greater energy dissipation rate than the classical self-similar solution emanating from the same Riemann data. We therefore show that the maximal dissipation criterion proposed by Dafermos does not favour in general the self-similar solutions.