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Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid

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Abstract

We study the non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid without viscosity. We first show that the life span of the classical solutions with decay at far fields must be finite for the 1D Cauchy problem if the initial momentum weight is positive. Then, we present several sufficient conditions for the non-existence of global classical solutions to the 1D initial-boundary value problem on [0, 1]. To prove these results, some new average quantities are introduced.

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Acknowledgments

The authors would like to thank the anonymous reviewer for his or her helpful suggestions, which have improved the quality of this paper greatly.

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Authors and Affiliations

  1. School of Mathematics, Zhengzhou University of Aeronautics, 100 Science Avenue, Zhengzhou, 450015, P. R. China

    Jianwei Dong, Junhui Zhu & Litao Zhang

Authors
  1. Jianwei Dong
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  2. Junhui Zhu
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  3. Litao Zhang
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Corresponding author

Correspondence to Jianwei Dong.

Additional information

This work is supported by the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province (2019GGJS176), the Vital Science Research Foundation of Henan Province Education Department (22A110024, 22A110026), the Scientific Research Team Plan of Zhengzhou University of Aeronautics (23ZHTD01003), the Basic Research Projects of Key Scientific Research Projects Plan in Henan Higher Education Institutions (20zx003) and the Henan Natural Science Foundation (222300420579).

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Dong, J., Zhu, J. & Zhang, L. Non-existence of global classical solutions to 1D compressible heat-conducting micropolar fluid. Czech Math J 74, 29–43 (2024). https://doi.org/10.21136/CMJ.2023.0196-22

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  • DOI: https://doi.org/10.21136/CMJ.2023.0196-22

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