Accession Number:

ADA129169

Title:

Nonexistence of a Shock Layer in Gas Dynamics with a Nonconvex Equation of State.

Descriptive Note:

Technical summary rept.,

Corporate Author:

WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s):

Report Date:

1983-04-01

Pagination or Media Count:

26.0

Abstract:

A classical result of Gilbarg states that a simple shock wave solution of Eulers equations in compressive if and only if a corresponding shock layer solution of the Navier-Stokes equations exists, assuming, among other things, that the equation of state is convex. An entropy condition appropriate for weeding out unphysical shocks in the nonconvex case has been introduced by Liu. For shocks satisfying his entropy condition, Liu showed that purely viscous shock layers exist with zero heat conduction. Dropping the convexity assumption, but retaining many other reasonable restrictions on the equation of state, Pego, the author constructs an example of a large amplitude shock which satisfies Lius entropy condition but for which a shock layer does not exist if heat conduction dominates viscosity. Pego also gives a simple restriction, weaker than convexity, which does guarantee that shocks which satisfy Lius entropy condition always admit shock layers. Author

Subject Categories:

  • Numerical Mathematics
  • Fluid Mechanics
  • Radiofrequency Wave Propagation

Distribution Statement:

APPROVED FOR PUBLIC RELEASE