References
- Acheritogaray M, Degond P, Frouvelle A, et al. Kinetic formulation and global existence for the Hall-Magneto-hydrodynamicssystem. Kinet. Relat. Models. 2011;4:901–918.
- Chae D, Degond P, Liu J. Well-posedness for Hall-magnetohydrodynamics. Ann. Inst. H. Poincaré Anal. Non Linéaire. 2014;31:555–565.
- Chae D, Lee J. On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics. J. Differ. Equ. 2014;256:3835–3858.
- Chae D, Schonbek M. On the temporal decay for the Hall-magnetohydrodynamic equations. J. Differ. Equ. 2013;255:3971–3982.
- Chen Q, Miao C. Existence theorem and blow-up criterion of the strong solutions to the two-fluid MHD equation in ℝ3. J. Differ. Equ. 2007;239:251–271.
- Chae D, Weng S. Singularity formation for the incompressible Hall-MHD equations without resistivity. Ann. Inst. H. Poincaré Anal. Non Linéaire. 2016;33:1009–1022.
- Fan J, Ahmad B, Hayat T, et al. On blow-up criteria for a new Hall-MHD system. Appl. Math. Comput. 2016;274:20–24.
- Fan J, Jia X, Nakamura G, et al. On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip effects. Z. Angew. Math. Phys. 2015;66:1695–1706.
- Fan J, Ahmad B, Hayat T, et al. On well-posedness and blow-up for the full compressible Hall-MHD system. Nonlinear Anal. Real World Appl. 2016;31:569–579.
- Lighthill M. Studies on magneto-hydrodynamic waves and other anisotropic wave motions. Philos. Trans. R. Soc. London Ser. A. 1960;252:397–430.
- Wan R, Zhou Y. On global existence, energy decay and blow-up criteria for the Hall-MHD system. J. Differ. Equ. 2015;259:5982–6008.
- Chae D, Wan R, Wu J. Local well-posedness for the Hall MHD equations with fractional magnetic diffusion. J. Math. Fluid Mech. 2015;17:627–638.
- Fan J, Li F, Nakamura G. Regularity criteria for the incompressible Hall-magnetohydrodynamic equations. Nonlinear Anal. 2014;109:173–179.
- Wang Y, Zuo W. On the blow-up criterion of smooth solutions for Hall-magnetohydrodynamics system with partial viscosity. Commun. Pure Appl. Anal. 2014;13:1327–1336.
- He F, Ahmad B, Hayat T, et al. On regularity criteria for the 3D Hall-MHD equations in terms of the velocity. Nonlinear Anal. Real World Appl. 2016;32:35–51.
- Ye Z. Regularity criterion for the 3D Hall-magnetohydrodynamic equations involving the vorticity. Nonlinear Anal. 2016;144:182–193.
- Yuan B, Zhang B. Blow-up criterion of strong solutions to the Navier-Stokes equations in Besov spaces with negative indices. J. Differ. Equ. 2007;242:1–10.
- Bahouri H, Chemin J-Y, Danchin R. Fourier analysis and nonlinear partial differential equations. Vol. 343. Grundlehren der mathematischen Wissenschaften. Heidelberg: Springer; 2011.
- Chemin J-Y. Perfect incompressible fluids. Vol. 14, Oxford lecture series in mathematics and its applications. New York (NY): Oxford University Press; 1998.
- Miao C, Wu J, Zhang Z. Littlewood-Paley theory and its applications in partial differential equations of fluid dynamics. Beijing: Science Press; 2012. Chinese
- Majda A, Bertozzi A. Vorticity and incompressible flow. Cambridge: Cambridge University Press; 2001.
- Kato T, Ponce G. Commutator estimates and the Euler and Navier-Stokes equations. Commun. Pure Appl. Math. 1988;41:891–907.