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The global classical solution to a 1D two-fluid model with density-dependent viscosity and vacuum

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Abstract

In this paper, we consider the initial-boundary problem for a 1D two-fluid model with density-dependent viscosity and vacuum. The pressure depends on two variables but the viscosity only depends on one of the densities. We prove the global existence and uniqueness of the classical solution in the one-dimensional space with large initial data and vacuum. We use a new Helmholtz free energy function and the material derivative of the velocity field to deal with the general pressure with two variables, without the equivalence condition. We also develop a new argument to handle the general viscosity.

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Acknowledgements

The first author was supported by the Shantou University funding (Grant No. NTF20025), and National Natural Science Foundation of China (Grant No. 12101386). The second author was supported by National Natural Science Foundation of China (Grant Nos. 12171160, 11771150 and 11831003), and Guangdong Basic and Applied Basic Research Foundation (Grant No. 2020B1515310015).

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Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, China

    Senming Chen

  2. School of Mathematics, South China University of Technology, Guangzhou, 510641, China

    Changjiang Zhu

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  1. Senming Chen
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  2. Changjiang Zhu
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Correspondence to Changjiang Zhu.

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Chen, S., Zhu, C. The global classical solution to a 1D two-fluid model with density-dependent viscosity and vacuum. Sci. China Math. 65, 2563–2582 (2022). https://doi.org/10.1007/s11425-021-1906-2

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  • DOI: https://doi.org/10.1007/s11425-021-1906-2

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