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

Yuzhu Wang

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

Published online: 2021-01

Export citation
  • 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 = {Yuzhu and Wang and wangyuzhu@ncwu.edu.cn and 10069 and School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China. and Yuzhu Wang}, 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 KW - global existence KW - 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.

Yuzhu Wang. (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
Copy to clipboard
The citation has been copied to your clipboard