Logarithmically improved regularity criterion for the Boussinesq equations in Besov spaces with negative indices

Abstract

The aim of this paper is to establish a logarithmically improved the regularity criterion in terms of the homogeneous Besov space to the Boussinesq equations. We prove the solution is smooth up to time provided that

for some and .

Keywords:

• regularity criterion
• Boussinesq equations

AMS Subject Classifications:

• 35Q35
• 76D03

Acknowledgements

The authors are glad to acknowledge their sincere thanks to the referee for his careful reading of the work and his many valuable comments and suggestions. The authors would like to express their sincere gratitude to Professor Yong Zhou and Bo-Qing Dong for their helpful discussions and for their many constructive suggestions.

Notes

No potential conflict of interest was reported by the authors.