an:01288862
Zbl 0922.35089
Harten, Ami; Lax, Peter D.; Levermore, C. David; Morokoff, William J.
Convex entropies and hyperbolicity for general Euler equations
EN
SIAM J. Numer. Anal. 35, No. 6, 2117-2127 (1998).
00057176
1998
j
35L60 76N15 65M12
compressible Euler equations; entropy solutions; strictly convex entropy density
The authors consider the compressible Euler equations that possess a family of generalized entropy densities of the form \(\rho f(\sigma)\), where \(\rho\) is the mass density, \(\sigma\) is the specific entropy, and \(f\) is an arbitrary function. They determine which \(\rho f(\sigma)\) are strictly convex for gases with an arbitrary equation of state. It is shown also that at every state with positive sound speed (i.e., where the Euler equations are hyperbolic) there exist strictly convex \(\rho f(\sigma)\). This observation establishes the converse of the general fact that the existence of a strictly convex entropy density implies hyperbolicity.
P.B.Dubovski?? (Moskva)