Low Regularity Well-Posedness for the 3D Generalized Hall-MHD System

In this paper, we obtain the local well-posedness for the 3D incompressible Hall-magnetohydrodynamics (Hall-MHD) system with Λ2αu$\varLambda^{2\alpha }u$ and Λ2βB$\varLambda^{2\beta }B$, 0<α≤1$0<\alpha \le 1$, 12<β≤1$\frac{1}{2}<\beta \le 1$. Our results improve regularity conditions on the initial data of previous works.

[1]  A. Majda,et al.  Vorticity and incompressible flow , 2001 .

[2]  Dongho Chae,et al.  On the temporal decay for the Hall-magnetohydrodynamic equations , 2013, 1302.4601.

[3]  Dongho Chae,et al.  Singularity formation for the incompressible Hall-MHD equations without resistivity , 2013, 1312.5519.

[4]  Yong Zhou,et al.  Regularity criteria for the incompressible Hall‐MHD system , 2015 .

[5]  Eric Dumas,et al.  On the Weak Solutions to the Maxwell–Landau–Lifshitz Equations and to the Hall–Magneto–Hydrodynamic Equations , 2013, Communications in Mathematical Physics.

[6]  R. Danchin,et al.  Fourier Analysis and Nonlinear Partial Differential Equations , 2011 .

[7]  Yong Zhou,et al.  On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip effects , 2015 .

[8]  L. Ferreira,et al.  Existence and stability of global large strong solutions for the Hall-MHD system , 2014, Differential and Integral Equations.

[9]  Tasawar Hayat,et al.  On well-posedness and blow-up for the full compressible Hall-MHD system , 2016 .

[10]  Tasawar Hayat,et al.  On regularity criteria for the 3D Hall-MHD equations in terms of the velocity , 2016 .

[11]  E. Stein.  Singular Integrals and Di?erentiability Properties of Functions , 1971 .

[12]  Gen Nakamura,et al.  Well-posedness for the axisymmetric incompressible viscous Hall-magnetohydrodynamic equations , 2013, Appl. Math. Lett..

[13]  Pierre Degond,et al.  Well-posedness for Hall-magnetohydrodynamics , 2012, 1212.3919.

[14]  Local Well-Posedness for the Hall-MHD Equations with Fractional Magnetic Diffusion , 2014, 1404.0486.

[15]  Tasawar Hayat,et al.  On blow-up criteria for a new Hall-MHD system , 2016, Appl. Math. Comput..

[16]  Andrew J. Majda,et al.  Vorticity and Incompressible Flow: Index , 2001 .

[17]  Pierre Degond,et al.  Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system , 2011 .

[18]  Ahmed Alsaedi,et al.  On strong solutions to the compressible Hall-magnetohydrodynamic system , 2015 .

[19]  Yong Zhou,et al.  On global existence, energy decay and blow-up criteria for the Hall-MHD system , 2015 .

[20]  Raphaël Danchin,et al.  Local and global well-posedness results for flows of inhomogeneous viscous fluids , 2004, Advances in Differential Equations.

[21]  Dongho Chae,et al.  On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics , 2013, 1305.4681.