Symmetric form of governing equations for capillary fluids

Sergey L. Gavrilyuk , Henri Gouin (1, 2)

1 LMMT - Laboratoire de Modélisation Mécanique et Thermodynamique, EA 2596
2 IUSTI - Institut universitaire des systèmes thermiques industriels

In classical continuum mechanics, quasi-linear systems of conservation laws can be symmetrized if they admit an additional convex conservation law. In particular, this implies the hyperbolicity of governing equations. For capillary fluids, the internal energy depends not only on the density but also on its derivatives with respect to space variables. Consequently, the governing equations belong to the class of dispersive systems. In that case we propose a symmetric form of governing equations which is different from the classical Godunov -Friedrichs - Lax representation. This new symmetric form implies the stability of constant solutions.

Mots clés: Hyperbolic systems; Structural stability; Partial differential equations; Fluid mechanics; Gas/liquid flows; Liquid-vapor transitions

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Dynamique des Fluides [physics.flu-dyn]

Sergey L. Gavrilyuk, Henri Gouin. Symmetric form of governing equations for capillary fluids. Monographs and Surveys in Pure and Applied Mathematics, 1999, Nice, France. pp.Pages 306-311. ⟨hal-00252237⟩