Global existence and large time behavior of weak solutions to the two-phase flow

2022/03/05 by Ya-Ting Wang, Wang, Ya-Ting, Ling-Yun Shou +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2203.02749

38 pages

arxiv created 2022/03/10 · arxiv updated 2022/03/11

Abstract

In this paper, we consider a two-phase flow model consisting of the compressible Navier-Stokes systems with degenerate viscosity coupled with the compressible Navier-Stokes systems with constant viscosities via a drag force, which can be derived from Chapman-Enskog expansion for the compressible Navier-Stokes-Vlasov-Fokker-Planck system. For general initial data, we establish the global existence of weak solutions with finite energy to the initial value problem in the three-dimensional periodic domain, and prove the convergence of global weak solutions to its equilibrium state as the time tends to infinity.

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