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

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 IS. 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 beta is an element of (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. (C) 2009 Elsevier Inc. All rights reserved.