Global Classical Solutions to the Two-phase Flow Model with Slip Boundary Condition in 3D Bounded Domains

Abstract

In this paper, we consider the two-phase flow model with slip boundary condition in a three-dimensional simply connected bounded domain with C^∞ boundary ∂Ω. The pressure depends on two different variables from the continuity equation. After discovering some new estimates on the boundary related to the slip boundary condition, we are able to obtain that the classical solutions to the initial-boundary-value problem of two-phase flow model exist globally in time provided that the initial energy is suitably small. As we know, this is the first result concerning the global existence of classical solutions to the compressible two-phase flow model with slip boundary condition and the density containing vacuum initially for general 3D bounded smooth domains.

Keywords

Two-fluid model / global existence / slip boundary condition / vacuum / 35B45 / 76N10 / 76T10

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