A global regularity result for the 2D Boussinesq equations with critical dissipation

Content Provider	Semantic Scholar
Author	Stefanov, Atanas Wu, Jiahong
Copyright Year	2014
Abstract	This paper examines the global regularity problem on the two-dimensional incompressible Boussinesq equations with fractional dissipation, given by Λαu in the velocity equation and by Λβθ in the temperature equation, where $\Lambda - \sqrt { - \Delta } $Λ−−Δ denotes the Zygmund operator. We establish the global existence and smoothness of classical solutions when (α, β) is in the critical range: $\alpha > (\sqrt {1777} - 23)/24 = 0.789103.$α>(1777−23)/24=0.789103., β > 0, and α + β = 1. This result improves previous work which obtained the global regularity for $\alpha > (23-\sqrt {145})/12 \approx 0.9132,\;\beta>0$α>(23−145)/12≈0.9132,β>0, and α + β = 1.
Starting Page	269
Ending Page	290
Page Count	22
File Format	PDF HTM / HTML
DOI	10.1007/s11854-018-0073-4
Volume Number	137
Alternate Webpage(s)	https://math.okstate.edu/people/jiahong/StefanovWu.pdf
Alternate Webpage(s)	https://arxiv.org/pdf/1411.1362v3.pdf
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article