Global weak solutions to one-dimensional non-conservative viscous compressible two-phase system. (English) Zbl 1235.76182
The authors deal with global weak solutions of a non-conservative viscous compressible two-phase model in one space dimension. The work extends in some sense a previous work [D. Bresch et al., Arch. Ration. Mech. Anal. 196, No. 2, 599–629 (2010; Zbl 1193.35146)], which provides the global existence of weak solutions in the multi-dimensional framework with \(1<\gamma_{\pm}<6\) assuming non-zero surface tension. In this study, one strongly improves the results by taking advantage of the one space dimension. More precisely, one obtains global existence of weak solutions without using capillarity terms and for pressure laws with the same range of coefficients as the degenerate barotropic mono-fluid system, namely \(\gamma_{\pm}>1\). Then one proves that any possible vacuum state has to vanish within finite time after which densities are always away from vacuum.
Reviewer: Titus Petrila (Cluj-Napoca)
Keywords:
global weak solutions; one-dimensional non-conservative viscous compressible; two-phase systemCitations:
Zbl 1193.35146References:
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