Free boundary value problem for a viscous two-phase model with mass-dependent viscosity
Free boundary value problem for a viscous two-phase model with mass-dependent viscosity
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DOI：
10.1016/j.jde.2009.07.013
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发表时间：
2009-11
影响因子：
2.4
通讯作者：
Lei Yao;Changjiang Zhu
中科院分区：
文献类型：
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作者：
Lei Yao;Changjiang Zhu
本文研究了具有质量相关粘性系数的两相气液两相模型的自由边值问题，其中初始液团和气团都间断地连接到真空中。这是文[S.Evje，K.H.Karlsen，具有奇异压力定律的粘性液气模型的整体弱解，http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV].]的推广就像[S.Evje，K.H.Karlsen，Global Share Solution for a粘性气液模型的奇异压力律，http://www.irisresearch.no/docsent/emp.nsf/wvAnsatte/SEV]，假定气体是多变的，而液体是不可压缩的流体。给出了当β∈(0，1]时弱解的整体存在唯一性的证明，改进了Evje和Karlsen以前的结果，得到了解的渐近性结果，并用能量方法得到了解的正则性。
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.