Open AccessOn the global existence to Hall-MHD system
Author(s) -
Lvqiao Liu
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2022044
Subject(s) - nabla symbol , magnetohydrodynamics , space (punctuation) , mathematics , physics , combinatorics , function (biology) , mathematical physics , magnetic field , quantum mechanics , omega , computer science , evolutionary biology , biology , operating system
This paper investigates the well-posedness of Hall-magnetohydrodynamics system. By using a new current function \begin{document}$ J = \nabla\times B $\end{document} as an additional unknown. The mild solution of Hall-MHD exists globally in the nonhomogeneous Lei-Lin space setting provided that the initial data satisfies \begin{document}$ \|u_{0}\|_{\mathcal{X}^{-1} }+\|B_{0}\|_{ \mathcal{X}^{-1}}+\|J_{0}\|_{ \mathcal{X}^{-1}}<\min \{\frac{\mu }{2}, \frac{\nu }{2}\}. $\end{document}