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Science China Mathematics

, Volume 62, Issue 3, pp 469–508 | Cite as

Existence and blow-up of the solutions to the viscous quantum magnetohydrodynamic nematic liquid crystal model

  • Guangwu WangEmail author
  • Boling Guo
Articles
  • 67 Downloads

Abstract

In this paper, we investigate the coupled viscous quantum magnetohydrodynamic equations and nematic liquid crystal equations which describe the motion of the nematic liquid crystals under the magnetic field and the quantum effects in the two-dimensional case. We prove the existence of the global finite energy weak solutions by use of a singular pressure close to vacuum. Then we obtain the local-in-time existence of the smooth solution. In the final, the blow-up of the smooth solutions is studied. The main techniques are Faedo-Galerkin method, compactness theory, Arzela-Ascoli theorem and construction of the functional differential inequality.

Keywords

viscous quantum magnetohydrodynamic equations nematic liquid crystal global weak solution singular pressure smooth solution blow-up 

MSC(2010)

35A01 35B44 35D30 35M11 35Q40 

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Notes

Acknowledgements

This work was supported by the Foundation of Guangzhou University (Grant No. 2700050357) and National Natural Science Foundation of China (Grant No. 11731014).

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceGuangzhou UniversityGuangzhouChina
  2. 2.Graduate School of China Academy of Engineering PhysicsBeijingChina
  3. 3.Institute of Applied Physics and Computational MathematicsChina Academy of Engineering PhysicsBeijingChina

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