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

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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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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Key words

  • Compressible quantum hydrodynamicmodel
  • blow-up criterion
  • strong solution

2010 MR Subject Classification

  • 35A01
  • 35D35
  • 35M30
  • 35Q40