THE GLOBAL STRONG SOLUTIONS OF THE 3D INCOMPRESSIBLE HALL-MHD SYSTEM WITH VARIABLE DENSITY-Reference-Cited by-同舟云学术

THE GLOBAL STRONG SOLUTIONS OF THE 3D INCOMPRESSIBLE HALL-MHD SYSTEM WITH VARIABLE DENSITY

Published:2024-03-26 Issue:2 Volume:29 Page:288-308
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
Short-container-title:

Author:

An Shu¹,Chen Jing²,Han Bin¹^ORCID

Affiliation:

1. Department of Mathematics, Hangzhou Dianzi University, Qiantang New District, 310018 Hangzhou, Zhejiang Province, China

2. School of Mathematics, Shanghai University of Finance and Economics, No. 777, Guoding Rd., Yangpu District, 200433 Shanghai, China

Abstract

In this paper, we focus on the well-posedness problem of the three-dimensional incompressible viscous and resistive Hall-magnetohydrodynamics system (Hall-MHD) with variable density. We mainly prove the existence and uniqueness issues of the density-dependent incompressible Hall-magnetohydrodynamic system in critical spaces on R3.

Publisher

Vilnius Gediminas Technical University

Reference34 articles.

1. H. Alfvén. Existence of electromagnetic-hydrodynamic waves. Nature, 150:405- 406, 1942. https://doi.org/10.1038/150405d0

2. M. Arichetogaray, P. Degond, A. Frouvelle and J.G. Liu. Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system. Kinetic and Related Models, 4(4):901-918, 2011. https://doi.org/10.3934/krm.2011.4.901

3. H. Bahouri, J.Y. Chemin and R. Danchin. Fourier analysis and nonlinear partial differential equations. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. 343, Springer, Heidelberg, 2011.

4. L.C. Campos. On hydromagnetic waves in atmospheres with application to the Sun. Ann. I. H. Poincaré, 10:37-70, 1998. https://doi.org/10.1007/s001620050050

5. D. Chae, P. Degond and J.G. Liu. Well-posedness for Hallmagnetohydrodynamics. Ann. I. H. Poincaré, 31(3):555-565, 2014. https://doi.org/10.1016/j.anihpc.2013.04.006