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The Global Solvability of the Non-conservative Viscous Compressible Two-Fluid Model with Capillarity Effects for Some Large Initial Data

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Abstract

The present paper is the continuation of works (Xu and Chi in Nonlinearity 34:164–204, 2021, Xu in The maximal regularity and its application to a multi-dimensional non-conservative viscous compressible two-fluid model with capillarity effects in \(L^{p}\)-type framework. arXiv:2201.05960, 2022). Under the assumption on the some large initial data, we obtain the existence of global strong solutions to a non-conservative viscous compressible two-fluid model with capillarity effects in any dimension \(N\ge 2\). Our analysis mainly relies on Fourier frequency localization technology, commutator estimate and Bony’s decomposition.

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Data and materials sharing not applicable to this article as no data and materials were generated or analyzed during the current study.

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Funding

This work is partially supported by the National Natural Science Foundation of China (11501332, 11771043,51976112), and the Natural Science Foundation of Shandong Province (ZR2021MA017).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, Shandong, China

    Fan Zhang & Fuyi Xu

  2. School of Agricultural Engineering and Food Science, Shandong University of Technology, Zibo, 255049, Shandong, China

    Peng Fu

Authors
  1. Fan Zhang
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  2. Fuyi Xu
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  3. Peng Fu
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Contributions

This work was carried out in collaboration of three authors. Xu proposed the question and presented some ideas of the proof. Zhang and Fu carried out the existence studies, and drafted the manuscript. All authors read and approved the final manuscript.

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Correspondence to Fuyi Xu.

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Communicated by D. Bresch.

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Zhang, F., Xu, F. & Fu, P. The Global Solvability of the Non-conservative Viscous Compressible Two-Fluid Model with Capillarity Effects for Some Large Initial Data. J. Math. Fluid Mech. 25, 53 (2023). https://doi.org/10.1007/s00021-023-00797-5

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