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Volume 34, Issue 1
Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity

Yuzhu Wang

DOI: 10.4208/jpde.v34.n1.1

J. Part. Diff. Eq., 34 (2021), pp. 1-13.

Published online: 2021-01

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  • Abstract

We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases new difficulty in proving global smooth solutions. Moreover, Hall term heightens the level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the initial data is enough small.

  • Keywords

Hall-MHD system with mixed viscosity, global existence, smooth solutions.

  • AMS Subject Headings

76D03, 76W05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wangyuzhu@ncwu.edu.cn (Yuzhu Wang)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-34-1, author = {Wang , Yuzhu}, title = {Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity}, journal = {Journal of Partial Differential Equations}, year = {2021}, volume = {34}, number = {1}, pages = {1--13}, abstract = {

We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases new difficulty in proving global smooth solutions. Moreover, Hall term heightens the level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the initial data is enough small.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v34.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/18551.html} }
TY - JOUR T1 - Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity AU - Wang , Yuzhu JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 13 PY - 2021 DA - 2021/01 SN - 34 DO - http://doi.org/10.4208/jpde.v34.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/18551.html KW - Hall-MHD system with mixed viscosity, global existence, smooth solutions. AB -

We investigate the global existence of smooth solutions to the three dimensional generalized Hall-MHD system with mixed partial viscosity in this work. The diffusion of mixed partial viscosity is weaker than that of full viscosity, which cases new difficulty in proving global smooth solutions. Moreover, Hall term heightens the level of nonlinearity of the standard MHD system. Global smooth solutions are established by using energy method and the bootstrapping argument, provided that the initial data is enough small.

Wang , Yuzhu. (2021). Global Existence of Smooth Solutions to Three Dimensional Hall-MHD System with Mixed Partial Viscosity. Journal of Partial Differential Equations. 34 (1). 1-13. doi:10.4208/jpde.v34.n1.1
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