On a Non-conservative Compressible Two-Fluid Model in a Bounded Domain: Global Existence and Uniqueness

Maximal Regularity for Compressible Two-Fluid System

“…Existence, uniqueness and stability of global weak solutions, still in one dimension, to system (1.1), has been shown by Li, Sun, Zatorska in [19] and some non-uniqeness results for the inviscid version of this system in multiple dimensions was shown by Li and Zatorska in [20]. Finally, let us also mention that very recently Wang, Wen and Yao proved global existence and uniqueness of solutions to the non-conservative two-fluid model with unequal velocities using the energy methods [31].…”

Global existence of weak solutions to the drift-flux system for general pressure laws

“…where α ± , ρ ± , u ± , P ± (ρ ± ), and τ ± denote the volume fractions, densities, velocities, pressures, and stress tensors of two fluids respectively. The global existence of weak solutions to (1.7) with degenerate viscosity coefficients was proved in [8,9] for P + (ρ + ) = P − (ρ − ), and the global well-posedness and optimal time-decay rates of strong solutions near the constant equilibrium state to (1.7) were studied in [22,48] for P + (ρ + ) = P − (ρ − ).…”

Remarks on global weak solutions to a two-fluid type model

“…Evje, Wang and Wen ([20]) found that the unequal pressure has stability effect for the Cauchy problem in three dimensions such that the strong solution with small initial data exists globally in time and decays algebraically. Very recently, Evje-Wang-Wen's results were extended by Wang, Wen and Yao ( [55]) to the Dirichlet problem.…”