A logarithmically improved regularity criterion for the 3D Hall-MHD equations in Besov spaces with negative indices

Abstract

In this paper we consider the three dimensional (3D) incompressible Hall-magnetohydrodynamic equations (Hall-MHD). It is proved that the local smooth solution can be continued beyond time T provided that the velocity u and the magnetic field B satisfy

for . As a consequence, this result extend the previous result.

Keywords:

• Hall-MHD equations
• regularity criterion
• Besov space

AMS Subject Classifications:

• 35Q35
• 35B65
• 76W05

Acknowledgements

The author would like to express the heartfelt thanks to the anonymous referees and the editor for their constructive comments and helpful suggestions that have contributed to the final preparation of the paper.

Notes

No potential conflict of interest was reported by the author.