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

Jin Lai; Huanyao Wen; Lei Yao

doi:10.3934/dcdsb.2017066

Article Contents

2017, Volume 22, Issue 4: 1361-1392. Doi: 10.3934/dcdsb.2017066

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

1.
School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an 710127, China
2.
School of Mathematics, South China University of Technology, Guangzhou, 510641, China, School of Mathematics and Center for Nonlinear Studies, Northwest University, Xi'an 710127, China

* Corresponding author: Lei Yao
* Corresponding author: Lei Yao

Received: February 2016

Revised: December 2016

Published: August 2017

Lai and Yao were supported by the National Natural Science Foundation of China #11571280,11331005, FANEDD #201315, Science and Technology Program of Shaanxi Province #2013KJXX-23, and China Scholarship Council. Wen was supported by the National Natural Science Foundation of China #11671150,11301205 and the Fundamental Research Funds for the Central Universities #D2154560.

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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.

Keywords:

Non-conservative compressible two-fluid model,
global existence and uniqueness,
vanishing capillarity limit,
energy estimates.

Mathematics Subject Classification: Primary:76T10, 76N10.

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References

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