Geodesic
Two-component viscous flows with density-dependent transition layer
Gabriele Witterstein1
1Technische Universität München, München Garching, Germany
Interfaces and free boundaries, Tome 11 (2009) no. 4, pp. 537-568

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DOI

We present a model describing flows which undergo a phase change caused by chemical reactions in the material flow. In mathematical terms, we consider a free boundary problem for the onedimensional, compressible Navier–Stokes system coupled with an Allen–Cahn equation. One free boundary arises at the boundary of the flow to a vacuum state with a jump in the density. Another approximate free boundary arises due to the Allen–Cahn equation modeling the phase transition of the flow. We consider a density-dependent viscosity μ=ρθ and a density-dependent transition layer of thickness δ=δ~ρ−1. We establish the existence of a unique weak global solution, provided that θ<1/3.
DOI : 10.4171/ifb/222
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Compressible Navier–Stokes equations, phase transition, variable transition layer, modeling biomaterials

Gabriele Witterstein  1

1 Technische Universität München, München Garching, Germany 
Gabriele Witterstein. Two-component viscous flows with density-dependent transition layer. Interfaces and free boundaries, Tome 11 (2009) no. 4, pp. 537-568. doi: 10.4171/ifb/222
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     author = {Gabriele Witterstein},
     title = {Two-component viscous flows with density-dependent transition layer},
     journal = {Interfaces and free boundaries},
     pages = {537--568},
     year = {2009},
     volume = {11},
     number = {4},
     doi = {10.4171/ifb/222},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/222/}
}
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