×

zbMATH — the first resource for mathematics

Stability of multi-dimensional phase transitions in a van der Waals fluid. (English) Zbl 0928.76015
The paper treats the Euler equations governing the isothermal compressible fluid with pressure law permitting the coexistence of liquid and vapor phases. The author considers weak solutions which involve propagating discontinuities connecting states in liquid phase to states in vapor phase. The dynamic stability of such propagating discontinuities, the so-called stability of dynamic phase transition, is also considered.

MSC:
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
82D15 Statistical mechanics of liquids
82B26 Phase transitions (general) in equilibrium statistical mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Majda, A., The stability of multi-dimensional shock fronts, Memoirs amer. math. soc., 41, No. 275, (1983) · Zbl 0506.76075
[2] Serre, D., ()
[3] Majda, A., The existence of multi-dimensional shock fronts, Memoirs amer. math. soc., 43, No. 281, (1983) · Zbl 0517.76068
[4] Kreiss, H.-O., Initial boundary value problems for hyperbolic systems, Comm. pure and applied maths, 23, 277-298, (1970) · Zbl 0193.06902
[5] Freistühler, H., A short note on the persistence of ideal shock waves. (Preprint.) Technische Hochschule Aachen.
[6] Hagan, R.; Slemrod, M., The viscosity-capillarity criterion for shocks and phase transitions, Arch. rational mech. anal., 83, 333-361, (1983) · Zbl 0531.76069
[7] Slemrod, M., An admissibility criterion for fluids exhibiting phase transitions, (), 423-432
[8] Slemrod, M., Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. rational mech. anal., 81, 301-315, (1983) · Zbl 0505.76082
[9] Truskinovsky, L., About the “normal growth” approximation in the dynamical theory of phase transitions, Continuum mech. thermodyn., 6, 185-208, (1994) · Zbl 0877.73006
[10] Kreiss, H.-O.; Lorenz, J., Initial-boundary problems and the Navier-Stokes equations, () · Zbl 0728.76084
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.