On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions

Huanyao Wen

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arXiv · 1902.05190

On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions

Huanyao Wen

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Abstract

We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure functions are of two components solving the continuity equations. Two typical cases for the pressure are considered, which are motivated by the compressible two-fluid model with possibly unequal velocities [3] and by a limiting system from the Vlasov-Fokker-Planck/compressible Navier-Stokes system [27] (see also some other relevant models like compressible MHD system for two-dimensional case [24] and compressible Oldroyd-B model with stress diffusion [1]). The lack of enough regularity for the two densities turns out some essential difficulties in the two-component pressure compared with the single-phase model, i.e., compressible Navier-Stokes equations. In this paper, the global existence theory does not require any domination conditions for the initial densities, which implies that transition to each single-phase flow is allowed.

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Huanyao Wen. 2019-02-14. On global solutions to a viscous compressible two-fluid model with unconstrained transition to single-phase flow in three dimensions. https://arxiv.org/abs/1902.05190

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