On the blow-up criterion for the 3D Boussinesq system with zero viscosity constant

Abstract

In this paper, we obtain a refined blow-up criterion in term of vorticity of fluid for smooth solutions to the 3D Boussinesq system with no viscosity term in the velocity equation, this criterion may admit more singular vorticity than previous ones do. Particularly, it improves Fan’s results.

Keywords:

• 3D Boussinesq system
• blow-up criterion
• zero viscosity

AMS Subject Classifications:

• 76B03
• 76D03
• 35B65

Acknowledgments

The author would like to thank the referees for their valuable comments and suggestions, which are very helpful for author to improve this paper.