Two-component viscous flows with density-dependent transition layer

  • Gabriele Witterstein

    Technische Universität München, München Garching, Germany


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.

Cite this article

Gabriele Witterstein, Two-component viscous flows with density-dependent transition layer. Interfaces Free Bound. 11 (2009), no. 4, pp. 537–568

DOI 10.4171/IFB/222