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Preprint 2012-003

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

Marshall Slemrod

Abstract: This article 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), (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 suggest that the cause of non-uniqueness for the weak solutions satisfying the second criterion is that the entropy inequality is not fully capturing information from kinetic theory.

Paper:
Available as PDF (174 Kbytes).
Author(s):
Marshall Slemrod
Submitted by:
; 2012-02-09.