1 results
Global regularity for the micropolar Rayleigh-Bénard problem with only velocity dissipation
- Part of
-
- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 152 / Issue 5 / October 2022
- Published online by Cambridge University Press:
- 26 August 2021, pp. 1109-1138
- Print publication:
- October 2022
-
- Article
- Export citation
-
This paper is concerned with the global regularity problem on the micropolar Rayleigh-Bénard problem with only velocity dissipation in
$\mathbb {R}^{d}$ with 
$d=2\ or\ 3$. By fully exploiting the special structure of the system, introducing two combined quantities and using the technique of Littlewood-Paley decomposition, we establish the global regularity of solutions to this system in 
$\mathbb {R}^{2}$. Moreover, we obtain the global regularity for fractional hyperviscosity case in 
$\mathbb {R}^{3}$ by employing various techniques including energy methods, the regularization of generalized heat operators on the Fourier frequency localized functions and logarithmic Sobolev interpolation inequalities.
