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.
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Gabriele Witterstein, Two-component viscous ﬂows with density-dependent transition layer. Interfaces Free Bound. 11 (2009), no. 4, pp. 537–568DOI 10.4171/IFB/222