In this article, we consider the tridimensional generalized Hall magneto-hydrodynamics (Hall-MHD) system, with $(-\Delta)^\alpha u$ and $(-\Delta)^\beta b$. For $\alpha\ge 5/4$, $\beta\ge 7/4$, we obtain the global regularity of classical solutions. For $0<\alpha<5/4$ and $1/2<\beta<7/4$, with small data, the system also possesses global classical solutions. In addition, for the standard Hall-MHD system, $\alpha=\beta=1$, by adding a suitable condition, we give a positive answer to the open question in [3]. At last, we study the regularity criterions of generalized Hall-MHD system. In particular, we prove the regularity criterion in terms of horizontal gradient $\nabla_{h}u,\nabla_{h}b$ for $1<\alpha<5/4$, $5/4\le\beta<7/4$
We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrod...
AbstractIn this paper we study the global regularity issue for the 3D incompressible MHD equations. ...
AbstractIn this letter, we consider the three-dimensional magnetohydrodynamic (3D MHD) equations and...
AbstractThis paper studies the regularity of generalized magneto-hydrodynamics equation on the condi...
We are concerned with the 3D incompressible Hall-magnetohydro-dynamic system (Hall-MHD). Our first a...
In this work, we study the blow-up criterion of the smooth solutions of three-dimensional incompress...
We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large sol...
We prove some regularity criteria for smooth solutions of the three-dimensional incompressible Hall-...
We study the regularity conditions for a weak solution to the incompressible 3D magnetohydrodynamic...
In this brief note we study the n-dimensional magnetohydrodynamic equations with hyper-viscosity and...
In this paper, we consider the global regularity of the three-dimensinal (3D) generalized magnetohyd...
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado...
In this work, we investigate the regularity criterion for the solution of the Hall-MHD system in thr...
In this paper, we consider the global regularity for the incompressible MHD-α system with fractional...
In this paper, we are dedicated to the global-in-time existence and uniqueness issues of solutions f...
We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrod...
AbstractIn this paper we study the global regularity issue for the 3D incompressible MHD equations. ...
AbstractIn this letter, we consider the three-dimensional magnetohydrodynamic (3D MHD) equations and...
AbstractThis paper studies the regularity of generalized magneto-hydrodynamics equation on the condi...
We are concerned with the 3D incompressible Hall-magnetohydro-dynamic system (Hall-MHD). Our first a...
In this work, we study the blow-up criterion of the smooth solutions of three-dimensional incompress...
We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large sol...
We prove some regularity criteria for smooth solutions of the three-dimensional incompressible Hall-...
We study the regularity conditions for a weak solution to the incompressible 3D magnetohydrodynamic...
In this brief note we study the n-dimensional magnetohydrodynamic equations with hyper-viscosity and...
In this paper, we consider the global regularity of the three-dimensinal (3D) generalized magnetohyd...
Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado...
In this work, we investigate the regularity criterion for the solution of the Hall-MHD system in thr...
In this paper, we consider the global regularity for the incompressible MHD-α system with fractional...
In this paper, we are dedicated to the global-in-time existence and uniqueness issues of solutions f...
We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrod...
AbstractIn this paper we study the global regularity issue for the 3D incompressible MHD equations. ...
AbstractIn this letter, we consider the three-dimensional magnetohydrodynamic (3D MHD) equations and...