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June  2018, 23(4): 1395-1410. doi: 10.3934/dcdsb.2018156

## Well-posedness in critical spaces for a multi-dimensional compressible viscous liquid-gas two-phase flow model

 1 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China 2 College of Science & Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, China 3 School of Mathematics, Sun Yat-Sen University, Guangzhou 510275, China

* Corresponding author

Received  August 2016 Revised  February 2018 Published  April 2018

Fund Project: Research Supported by the NNSF of China (Grant Nos. 11601164, 11271381 and 11701325), the National Basic Research Program of China (973 Program) (Grant No. 2010CB808002), the Natural Science Foundation of Fujian Province of China (Grant Nos. 2016J05010 and 2017J05007) and the Scientific Research Funds of Huaqiao University (Grant No.15BS201)

This paper is dedicated to the study of the Cauchy problem for a compressible viscous liquid-gas two-phase flow model in $\mathbb{R}^N\,(N≥2)$. We concentrate on the critical Besov spaces based on the $L^p$ setting. We improve the range of Lebesgue exponent $p$, for which the system is locally well-posed, compared to [22]. Applying Lagrangian coordinates is the key to our statements, as it enables us to obtain the result by means of Banach fixed point theorem.

Citation: Haibo Cui, Qunyi Bie, Zheng-An Yao. Well-posedness in critical spaces for a multi-dimensional compressible viscous liquid-gas two-phase flow model. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1395-1410. doi: 10.3934/dcdsb.2018156
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