an:06479804
Zbl 1405.35171
Ye, Zhuan; Xu, Xiaojing
Remarks on global regularity of the 2D Boussinesq equations with fractional dissipation
EN
Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 125, 715-724 (2015).
00348015
2015
j
35Q35 35B65 76D03
2D Boussinesq equations; fractional dissipation; global regularity
Summary: In this paper, we are interested in the study of the Cauchy problem to the two-dimensional (2D) incompressible Boussinesq equations with fractional dissipation. By making use of the nonlinear lower bounds for the fractional Laplacian established in [\textit{P. Constantin} and \textit{V. Vicol}, Geom. Funct. Anal. 22, No. 5, 1289--1321 (2012; Zbl 1256.35078)], we establish the global regularity of the smooth solutions of the 2D Boussinesq equations with a new range of fractional powers of the Laplacian. This result significantly improves the recent works of Constantin and Vicol [loc. cit.] and \textit{W. Yang} et al. [J. Differ. Equations 257, No. 11, 4188--4213 (2014; Zbl 1300.35108)].
Zbl 1256.35078; Zbl 1300.35108