Global regularity results for the 212D magnetic Bénard system with mixed partial viscosity

ABSTRACT

This paper studies the global regularity for the ${\displaystyle 2\frac{1}{2}}$D magnetic Bénard system with mixed partial viscosity. More precisely, we first show the global regularity for the ${\displaystyle 2\frac{1}{2}}$D magnetic Bénard system with zero thermal diffusivity by a well-known property of Hardy space and BMO. Moreover, resorting to the method of the local-in-time analysis, the global regularity for the ${\displaystyle 2\frac{1}{2}}$D magnetic Bénard system with zero thermal diffusivity and horizontal magnetic diffusion as well as vertical magnetic diffusion are also obtained.

KEYWORDS:

• ${\displaystyle 2\frac{1}{2}}$D
• magnetic Bénard system
• global regularity
• Cauchy problem
• partial viscosity

AMS SUBJECT CLASSIFICATIONS:

• 35A01
• 35B65
• 35Q35
• 76D03

Notes

No potential conflict of interest was reported by the author.