an:07159430
Zbl 1433.35265
Dong, Bo-Qing; Ye, Zhuan; Zhai, Xiaoping
Global regularity for the 2D Boussinesq equations with temperature-dependent viscosity
EN
J. Math. Fluid Mech. 22, No. 1, Paper No. 2, 16 p. (2020).
00444951
2020
j
35Q35 35B65 76D03 35R11 42B25
Boussinesq equations; variable viscosity; global regularity
Summary: This paper is devoted to the global regularity for the Cauchy problem of the two-dimensional Boussinesq equations with the temperature-dependent viscosity. We prove the global solutions for this system with any positive power of the fractional Laplacian for temperature under the assumption that the viscosity coefficient is sufficiently close to some positive constant. Our obtained result improves considerably the recent results in [\textit{H. Abidi} and \textit{P. Zhang}, Adv. Math. 305, 1202--1249 (2017; Zbl 1353.35220)] and [\textit{X. Zhai} et al., J. Differ. Equations 267, No. 1, 364--387 (2019; Zbl 1414.35153)]. In addition, a regularity criterion via the velocity is also obtained for this system without the above assumption on the viscosity coefficient.
Zbl 1353.35220; Zbl 1414.35153