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Stability of subsonic planar phase boundaries in a van der Waals fluid. (English) Zbl 0980.76023
The author considers the structural stability of dynamic phase changes occuring across sharp interfaces in a multidimensional van der Waals fluid. Such phase transitions can be viewed as propagating discontinuities. One uses usually an additional jump condition, which can be derived from the viscosity-capillarity criterion. The aim of this paper is to point out the role of vicosity in the stability analysis, in order to deal with more realistic dissipative phase transitions. The main difficulty lies in the above additional jump condition, which is no longer explicit and depends on the (unknown) internal structure of the interface. This difficulty is overcomed by using bifurcation arguments for a nondimensional parameter measuring the competition between the viscosity and capillarity. The dissipative plane phase boundaries are shown to be uniformly linearly stable.

MSC:
76E17 Interfacial stability and instability in hydrodynamic stability
82D15 Statistical mechanics of liquids
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