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Journal of Mathematical Fluid Mechanics

, Volume 17, Issue 4, pp 769–797 | Cite as

On Two-Dimensional Magnetic Bénard Problem with Mixed Partial Viscosity

  • Jianfeng Cheng
  • Lili DuEmail author
Article

Abstract

In this paper, we deal with the Cauchy problem of the two-dimensional magnetic Bénard problem with mixed partial viscosity. More precisely, the global well-posedness of 2D magnetic Bénard problem without thermal diffusivity and with vertical or horizontal magnetic diffusion is obtained. Moreover, the global regularity and some conditional regularity of strong solutions are obtained for 2D magnetic Bénard problem with mixed partial viscosity. The results extend the recent work (Appl Math Letter 26:627–630, 2013) on the global regularity of the magnetic Bénard problem with full dissipation and magnetic diffusion in two dimensions.

Keywords

Cauchy Problem Regularity Criterion Global Regularity Unique Classical Solution Boussinesq System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of MathematicsSichuan UniversityChengduPeople’s Republic of China

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