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Discrete and Continuous Dynamical Systems - Series B (DCDS-B)
 

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

Pages: 1361 - 1392, Volume 22, Issue 4, June 2017      doi:10.3934/dcdsb.2017066

 
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Jin Lai - School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an 710127, China (email)
Huanyao Wen - School of Mathematics, South China University of Technology, Guangzhou, 510641, China (email)
Lei Yao - School of Mathematics, South China University of Technology, Guangzhou, 510641, China (email)

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 $\sigma^+$ and $\sigma^-$, 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 $\sigma^+$ 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:  Non-conservative compressible two-fluid model, global existence and uniqueness, vanishing capillarity limit, energy estimates.
Mathematics Subject Classification:  Primary: 76T10, 76N10.

Received: February 2016;      Revised: December 2016;      Available Online: February 2017.

 References