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Volume 33, Issue 2
Blow-Up Solution of the 3D Viscous Incompressible MHD System

Xin-Guang Yang, Wei Shi & Yongjin Lu

DOI: 10.4208/jpde.v33.n2.2

J. Part. Diff. Eq., 33 (2020), pp. 109-118.

Published online: 2020-05

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  • Abstract

The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwell equation. The global well-posedness of the coupled system is still an open problem. In this paper, we study the Cauchy problem of this coupled system and establish some logarithmical type of blow-up criterion for smooth solution in Lorentz spaces.

  • Keywords

MHD equations, blow-up criteria, Lorentz space.

  • AMS Subject Headings

35B40, 35B41, 35Q30, 76D03, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

yangxinguang@hotmail.com (Xin-Guang Yang)

18238105961@163.com (Wei Shi)

ylu@vsu.edu (Yongjin Lu)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-33-109, author = {Yang , Xin-GuangShi , Wei and Lu , Yongjin}, title = {Blow-Up Solution of the 3D Viscous Incompressible MHD System}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {2}, pages = {109--118}, abstract = {

The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwell equation. The global well-posedness of the coupled system is still an open problem. In this paper, we study the Cauchy problem of this coupled system and establish some logarithmical type of blow-up criterion for smooth solution in Lorentz spaces.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n2.2}, url = {http://global-sci.org/intro/article_detail/jpde/16854.html} }
TY - JOUR T1 - Blow-Up Solution of the 3D Viscous Incompressible MHD System AU - Yang , Xin-Guang AU - Shi , Wei AU - Lu , Yongjin JO - Journal of Partial Differential Equations VL - 2 SP - 109 EP - 118 PY - 2020 DA - 2020/05 SN - 33 DO - http://doi.org/10.4208/jpde.v33.n2.2 UR - https://global-sci.org/intro/article_detail/jpde/16854.html KW - MHD equations, blow-up criteria, Lorentz space. AB -

The 3D viscous incompressible magneto-hydrodynamic (MHD) system comprised by the 3D incompressible viscous Navier-Stokes equation couples with Maxwell equation. The global well-posedness of the coupled system is still an open problem. In this paper, we study the Cauchy problem of this coupled system and establish some logarithmical type of blow-up criterion for smooth solution in Lorentz spaces.

Xin-Guang Yang, Wei Shi & Yongjin Lu. (2020). Blow-Up Solution of the 3D Viscous Incompressible MHD System. Journal of Partial Differential Equations. 33 (2). 109-118. doi:10.4208/jpde.v33.n2.2
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