Blow-up criterion for 3D viscous liquid–gas two-phase flow model

Abstract

This work deals with the blow-up criterion for the strong solution to the three-dimensional viscous liquid–gas two-phase flow model in terms of the L1(0,T;L∞)-norm of the gradient of the velocity with two types of boundary conditions: the Dirichlet boundary condition and the Navier-slip boundary condition. There is no extra restriction on viscosity coefficients. The result also applies to the whole space case.