Vanishing capillarity limit of the non-conservative compressible two-fluid model

Abstract

In this paper, we consider the non-conservative compressible two-fluid model with constant viscosity coefficients and unequal pressure function in $\mathbb{R}^3$, we study the vanishing capillarity limit of the smooth solution to the initial value problem. We first establish the uniform estimates of global smooth solution with respect to the capillary coefficients $σ^+$ and $σ^-$, then by the Lion-Aubin lemma, we can obtain the unique smooth solution of the 3D non-conservative compressible two-fluid model with the capillary coefficients converges globally in time to the smooth solution of the 3D generic two-fluid model as $σ^+$ and $σ^-$ tend to zero. Also, we give the convergence rate estimates with respect to the capillary coefficients $σ^+$ and $σ^-$ for any given positive time.