Differential and Integral Equations

Existence of global weak solutions for compressible fluid models with a capillary tensor for discontinuous interfaces

Boris Haspot

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Abstract

This work is devoted to proving the global existence of weak solutions for a general isothermal model of capillary fluids derived in his modern form by C. Rohde in [21], which can be used as a phase transition model. First, inspired by the result by P.-L. Lions in [19] on the Navier-Stokes compressible system we show the global stability of weak solutions for our system with isentropic pressure and next with general pressure. Finally, we consider perturbations of a stable equilibrium.

Article information

Source
Differential Integral Equations, Volume 23, Number 9/10 (2010), 899-934.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019117

Mathematical Reviews number (MathSciNet)
MR2675587

Zentralblatt MATH identifier
1240.35404

Subjects
Primary: 35D30: Weak solutions 35Q35: PDEs in connection with fluid mechanics 35D05

Citation

Haspot, Boris. Existence of global weak solutions for compressible fluid models with a capillary tensor for discontinuous interfaces. Differential Integral Equations 23 (2010), no. 9/10, 899--934. https://projecteuclid.org/euclid.die/1356019117


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