A regularity criterion for the 3D Boussinesq equations

ABSTRACT

In this paper, we consider the regularity criteria of 3D incompressible Boussinesq equations. By using the Littlewood–Paley decomposition technique to establishing a regularity criterion in terms of the one-directional derivative of velocity in Besov spaces. Our result improves some previous works (Liu Q. A regularity criterion for the Navier–Stokes equations in terms of one-directional derivative of the velocity. Acta Appl Math. 2015;140(1):1–9; Gala S, Ragusa M A. On the regularity criterion for the Navier–Stokes equations in terms of one-directional derivative. Asian-Eur J Math. 2017;10(1):1750012).

Keywords:

• Boussinesq equations
• regularity criteria
• Besov spaces

2010 Mathematics Subject Classifications:

• 35Q35
• 35B65
• 76D03

Acknowledgments

The author would like to acknowledge his sincere thanks to the editor and the referees for a careful reading of the work and many valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.