Compressible Euler equations with general pressure law
The authors consider one-dimensional Euler equations of isentropic compressible fluid, and prove the existence of entropy solutions. Pressure is a general function of density. The only restriction is that the pressure law corresponds to a polytropic perfect gas asymptotically near vacuum. Approximate solutions are constructed by the vanishing artificial viscosity method or by the Lax-Friedrichs difference scheme. The proof of compactness of approximate solutions involves Tartar commutation relations for entropy pairs. The same method is applied for the proof of compactness of bounded entropy solutions. An imbalance of regularity of different parts of Tartar relations is used. To this end, singularities are studied for fractional derivatives of weak entropies, and for the corresponding entropy fluxes. Finally, the authors investigate the large-time behavior of entropy solutions.
compactness of bounded entropy solutions
scientific article; zbMATH DE number 1501926