A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

doi:10.1007/s10473-020-0314-3

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 795-804.doi: 10.1007/s10473-020-0314-3

A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

王光武¹, 郭柏灵²

1 School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2 Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing 100088, China

收稿日期:2019-01-14 出版日期:2020-06-25 发布日期:2020-07-17
通讯作者: Guangwu WANG E-mail:yunxianwgw@163.com
作者简介:Boling GUO,E-mail:gbl@iapcm.ac.cn
基金资助:
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).

A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

Guangwu WANG¹, Boling GUO²

1 School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China;
2 Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing 100088, China

Received:2019-01-14 Online:2020-06-25 Published:2020-07-17
Contact: Guangwu WANG E-mail:yunxianwgw@163.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Compressible quantum hydrodynamic model, blow-up criterion, strong solution

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.

Key words: Compressible quantum hydrodynamic model, blow-up criterion, strong solution

中图分类号:

35A01

王光武, 郭柏灵. A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL[J]. 数学物理学报(英文版), 2020, 40(3): 795-804.

Guangwu WANG, Boling GUO. A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL[J]. Acta mathematica scientia,Series B, 2020, 40(3): 795-804.

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A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

A BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE QUANTUM HYDRODYNAMIC MODEL

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