Vanishing capillarity limit of the nonconservative compressible twofluid model
Jin Lai  School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an 710127, China (email) Abstract: In this paper, we consider the nonconservative compressible twofluid 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 $\sigma^+$ and $\sigma^$, then by the LionAubin lemma, we can obtain the unique smooth solution of the 3D nonconservative compressible twofluid model with the capillary coefficients converges globally in time to the smooth solution of the 3D generic twofluid model as $\sigma^+$ and $\sigma^$ tend to zero. Also, we give the convergence rate estimates with respect to the capillary coefficients $\sigma^+$ and $\sigma^$ for any given positive time.
Keywords: Nonconservative compressible twofluid model, global existence and uniqueness, vanishing capillarity limit, energy estimates.
Received: February 2016; Revised: December 2016; Available Online: February 2017. 
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