On the continuation principle of local smooth solution for the Hall-MHD equations

ABSTRACT

This work deals with the blow-up criterion of local smooth solution to the 3D Hall-magnetohydrodynamics equations in Besov spaces ${\dot{B}}_{\mathrm{\infty },\mathrm{\infty }}^0$.

KEYWORDS:

• Hall-magnetohydrodynamic equations
• Besov space
• blow-up criterion

MATHEMATICS SUBJECT CLASSIFICATIONS(2000):

• 35Q35
• 35B65
• 76D05

Acknowledgments

This work This work was done while Sadek GALA was visiting the Catania University in Italy. He would like to thank the hospitality and support of the University, where this work was completed. This paper is partially supported by GNAMPA 2019. Maria Alessandra Ragusa wishes to thank the support of ‘RUDN University Program 5-100’. The authors are indebted with Prof. Yong Zhou for having drawn his attention to the above problem and for useful discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This paper is partially supported by GNAMPA 2019.