Flows of perfect fluids having two independent space-like variables. Reflection of a plane shock by a compressible wedge. (Écoulements de fluides parfaits en deux variables indépendantes de type espace. Réflexion d’un choc plan par un dièdre compressif.) (French) Zbl 0838.76077

Serre, Denis

Arch. Ration. Mech. Anal. 132, No. 1, 15-36 (1995).

Summary: We consider the Euler equations of a perfect fluid having only two independent space-like variables, which account for the stationary two-dimensional or axisymmetrical three-dimensional cases as well as the two-dimensional Riemann problem. We show that the pressure and the angle between an axis and the velocity field satisfy a first-order system which turns out to be elliptic in the subsonic zone. In particular, the pressure satisfies a maximum principle which has not been stated before, to the best of my knowledge. Using this and the Bernoulli law, we give various a priori estimates of the pressure, the density, the enthalpy, and the velocity in the problem of the reflection of a shock wave by a wedge. We also bound the size of the subsonic region and the force that the fluid applies to the boundary.

MSC:

76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76L05	Shock waves and blast waves in fluid mechanics
35Q35	PDEs in connection with fluid mechanics

Keywords:

Euler equations; Riemann problem; maximum principle; Bernoulli law; a priori estimates; subsonic region

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