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

  • * Corresponding author: Lei Yao

    * Corresponding author: Lei Yao
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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  • 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.

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


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