We prove local existence of smooth solutions for large data and global smooth solutions for
small data to the incompressible, resistive, viscous or inviscid Hall-MHD model. We also …

In this paper, we establish an optimal blow-up criterion for classical solutions to the
incompressible resistive Hall-magnetohydrodynamic equations. We also prove two global-in …

We establish temporal decay estimates for weak solutions to the Hall-magnetohydrodynamic
equations. With these estimates in hand we obtain algebraic time decay for higher order …

In this paper, we obtain global existence and energy decay for 3D Hall-
magnetohydrodynamics (Hall-MHD) system with− Δ u and− Δ B. Besides the classical …

Abstract The Hall-magnetohydrodynamics (Hall-MHD) equations, rigorously derived from
kinetic models, are useful in describing many physical phenomena in geophysics and …

In this paper we show that the incompressible Hall-MHD system without resistivity is not
globally in time well-posed in any Sobolev space H m (R 3) for any m> 7 2. Namely, either …

We investigate the existence and uniqueness issues of the 3D incompressible Hall-
magnetohydrodynamic system supplemented with initial velocity u 0 and magnetic field B 0 …

In this paper, we address the space–time decay properties for strong solutions to the
incompressible viscous resistive Hall-MHD equations. We obtained the same space–time …

On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip
effects Page 1 Z. Angew. Math. Phys. 66 (2015), 1695–1706 c© 2015 Springer Basel 0044-2275/15/041695-12 …

In this paper we study Liouville properties of smooth steady axially symmetric solutions of
the Navier-Stokes equations. First, we provide another version of the Liouville theorem …