Admissibility of weak solutions for the compressible Euler equations, n ≥ 2

This paper compares three popular notions of admissibility for weak solutions of the compressible isentropic Euler equations of gas dynamics: (i) the viscosity criterion, (ii) the entropy inequality (the thermodynamically admissible isentropic solutions), and (iii) the viscosity-capillarity criterion. An exact summation of the Chapman-Enskog expansion for Grad's moment system suggests that it is the third criterion that is representing the kinetic theory of gases. This, in turn, may shed some light on the ability to recover weak solutions of the Euler equations via a hydrodynamic limit.