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Blow-up of Smooth Solutions to the Cauchy Problem for the Viscous Two-Phase Model

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Abstract

In this paper, we will show the blow-up of smooth solutions to the Cauchy problem for the viscous two-phase model in arbitrary dimensions under some restrictions on the initial data. The key of the proof is finding the relations between some physical quantities and establishing some inequalities.

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Acknowledgments

The authors acknowledge support from the Outstanding Youth Foundation of Science and Technology Innovation of Henan Province (2018JQ0004), the Aeronautical Science Foundation of China (2017ZD55014), the Project of Youth Backbone Teachers of Colleges and Universities in Henan Province (2013GGJS-142) and NSFC(11501525).

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Authors and Affiliations

  1. School of Mathematics and Physics, Zhengzhou University of Aeronautics, Zhengzhou, 450015, People’s Republic of China

    Jianwei Dong, Junhui Zhu & Hongxia Xue

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  1. Jianwei Dong
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  2. Junhui Zhu
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  3. Hongxia Xue
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Correspondence to Jianwei Dong.

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Dong, J., Zhu, J. & Xue, H. Blow-up of Smooth Solutions to the Cauchy Problem for the Viscous Two-Phase Model. Math Phys Anal Geom 21, 20 (2018). https://doi.org/10.1007/s11040-018-9279-z

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  • DOI: https://doi.org/10.1007/s11040-018-9279-z

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