Global smooth solutions to the 3D generalized Hall-magnetohydrodynamic equations with large data

Abstract

In this paper, based on a perturbation argument and fully exploring the nonlinear structure of the considered system, we establish the global existence to the three-dimensional generalized incompressible Hall-MHD equations for a class of large initial data, whose $L^p,1\le p\le \mathrm{\infty }$ norms can be arbitrarily large. Our obtained result improves considerably the recent result in Li et al. [A class large solution of the 3D Hall-magnetohydrodynamic equations. J Differ Equ. 2020;268(10):5811–5822] to the generalized Hall-MHD system with $0\le \alpha \le 1$ equipping with different viscosity and magnetic diffusion coefficients.

Keywords:

• Generalized Hall-MHD equations
• global existence
• large initial data

2010 Mathematics Subject Classifications:

• 35Q35
• 76D03

Acknowledgments

The authors are grateful to the referees for helpful comments and suggestions that greatly improved the presentation of this paper.

Disclosure statement

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

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11801090] and Postdoctoral Science Foundation of China [2020T130129 and 2020M672565].