Free boundary value problem for a viscous two-phase model with mass-dependent viscosity

Abstract In this paper, we study a free boundary value problem for two-phase liquid–gas model with mass-dependent viscosity coefficient when both the initial liquid and gas masses connect to vacuum with a discontinuity. This is an extension of the paper [S. Evje, K.H. Karlsen, Global weak solutions for a viscous liquid–gas model with singular pressure law, http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV ]. Just as in [S. Evje, K.H. Karlsen, Global weak solutions for a viscous liquid–gas model with singular pressure law, http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV ], the gas is assumed to be polytropic whereas the liquid is treated as an incompressible fluid. We give the proof of the global existence and uniqueness of weak solutions when β ∈ ( 0 , 1 ] , which have improved the previous result of Evje and Karlsen, and get the asymptotic behavior result, also we obtain the regularity of the solutions by energy method.

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