- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
13
2011
4
Distributional equation in the limit of phase transition for fluids
Hans Wilhelm
Alt
Universität Bonn, BONN, GERMANY
Gabriele
Witterstein
Technische Universität München, MÜNCHEN GARCHING, GERMANY
Compressible Navier–Stokes equations; phase transition; sharp interface model
We study the convergence of a diffusive interface model to a sharp interface model. The model consists of the conservation of mass and momentum, where the mass undergoes a phase transition. The equations were considered in [W3] and in the diffuse case consist of the compressible Navier–Stokes system coupled with an Allen–Cahn equation. In the sharp interface limit a jump in the mass density as well as in the velocity occurs. The convergence of mass and momentum is considered in the distributional sense. The convergence of the free energy to a limit is shown in a separate paper. The procedure in this paper works also in other general situations.
Statistical mechanics, structure of matter
Partial differential equations
General
531
554
10.4171/IFB/271
http://www.ems-ph.org/doi/10.4171/IFB/271