Vanishing Capillarity Limit Of The Non-conservative Compressible Two-fluid Model

In this paper,we consider the non-conservative compressible two-fluid mod-el with constant viscosity coefficients and unequal pressure function in R3 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 ?~+ and ?~-,then by the Lion-Aubin lemma,we can obtain the unique smooth solution of the 3D non-conservative compress-ible two-fluid model with the capillary coefficients converges globally in time to the smooth solution of the 3D generic two-fluid model as ?~+ and ?~-tend to zero.Also,we give the convergence rate estimates with respect to the capillary coefficients ?~+ and ?~-for any given positive time.Specifically,the main results as follows:? The initial value problem of this model in 3D has been investigated,we obtain the global existence of smooth solution.? Based on the a priori estimates of global smooth solution with respect to the capillary coefficients ?~+ and ?~-,we obtain the global smooth solution of this model converges to the smooth solution of the generic two-fluid model as ?~+ and?~-tend to zero.? The convergence rate estimates with respect to ?~+ and ?~-of the global smooth solution for this model to the generic two-fluid model have been investigated.