Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (1): 413-432.doi: 10.1016/S0252-9602(12)60026-5

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FREE BOUNDARY VALUE PROBLEM OF ONE DIMENSIONAL TWO-PHASE LIQUID-GAS MODEL

 WANG Zhen, ZHANG Hui   

  1. Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China
  • Received:2012-01-04 Online:2012-01-20 Published:2012-01-20
  • Supported by:

    Supported by the National Natural Science Foundation of China (11171340).

Abstract:

In this paper, we study a free boundary value problem for two-phase liquid-gas model with mass-dependent viscosity coeffcient when both the initial liquid and gas masses connect to vacuum continuously. 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 result of Evje and
Karlsen, and we obtain the regularity of the solutions by energy method.

Key words: two-phase flow, weak solutions, Lagrangian coordinates, free boundaryprob-lem, vacuum, uniqueness

CLC Number: 

  • 35B40
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