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A Blow-Up Criterion of Strong Solutions to the Quantum Hydrodynamic Model

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Abstract

In this article, we focus on the short time strong solution to a compressible quantum hydrodynamic model. We establish a blow-up criterion about the solutions of the compressible quantum hydrodynamic model in terms of the gradient of the velocity, the second spacial derivative of the square root of the density, and the first order time derivative and first order spacial derivative of the square root of the density.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

    Wang Guangwu  (王光武)

  2. Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing, 100088, China

    Guo Boling  (郭柏灵)

Authors
  1. Wang Guangwu  (王光武)
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  2. Guo Boling  (郭柏灵)
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Corresponding author

Correspondence to Wang Guangwu  (王光武).

Additional information

The first author is supported by the National Natural Science Foundation of China (11801107); the second author is supported by the National Natural Science Foundation of China (11731014).

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Guangwu, W., Boling, G. A Blow-Up Criterion of Strong Solutions to the Quantum Hydrodynamic Model. Acta Math Sci 40, 795–804 (2020). https://doi.org/10.1007/s10473-020-0314-3

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  • DOI: https://doi.org/10.1007/s10473-020-0314-3

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