Abstract
In this paper, we study a two-phase liquid–gas model with constant viscosity coefficient when both the initial liquid and gas masses connect to vacuum continuously. Just as in Evje and Karlsen (Commun Pure Appl Anal 8:1867–1894, 2009) and Evje et al. (Nonlinear Anal 70:3864–3886, 2009), the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We use a new technique to get the upper and lower bounds of gas and liquid masses n and m. Then we get the global existence of weak solution by the line method. Also, we obtain the uniqueness of the weak solution.
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Yao, L., Zhu, C.J. Existence and uniqueness of global weak solution to a two-phase flow model with vacuum. Math. Ann. 349, 903–928 (2011). https://doi.org/10.1007/s00208-010-0544-0
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DOI: https://doi.org/10.1007/s00208-010-0544-0