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Global regularity of 2D MHD equations with almost Laplacian velocity dissipation
We obtain the global existence and global regularity for the 2D MHD equations with almost Laplacian velocity dissipation, which require the...
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Time Optimal Control Problem of the 2D MHD Equations with Memory
In this paper, we study an optimal control problem for the 2D MHD equations with memory in bounded domains with Dirichlet boundary conditions, where...
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The Global Well-posedness of Strong Solutions to 2D MHD Equations in Lei-Lin Space
In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a...
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Regularization by transport noises for 3D MHD equations
We consider the problem of regularization by noises for the three-dimensional magnetohydrodynamical (3D MHD) equations. It is shown that in a...
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On Some Recent Results from the Theory of MHD Equations
This chapter shows the main ideas of the derivation of the MHD and Hall–MHD equations (Sect. 1) and provides a brief survey of qualitative properties...
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Computational analysis for fractional characterization of coupled convection-diffusion equations arising in MHD flows
The work is devoted to the fractional characterization of time-dependent coupled convection-diffusion systems arising in magnetohydrodynamics (MHD)...
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Some Liouville-Type Results for the 3D Incompressible MHD Equations
In this paper, we investigate some Liouville-type properties for the stationary incompressible MHD equations in three dimensions. Liouville-type...
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Global Well-Posedness and Asymptotic Behavior of the 3D MHD-Boussinesq Equations
In this paper, we study global well-posedness of the three-dimensional MHD-Boussinesq equations. The global existence of axisymmetric strong...
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Global Regularity of 2D Incompressible Magneto-Micropolar Fluid Equations with Partial Viscosity
This paper studies the global regularity of 2D incompressible anisotropic magneto-micropolar fluid equations with partial viscosity. Ma [22] (Ma L....
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Shock Formation for 2D Isentropic Euler Equations with Self-similar Variables
The author studies the 2D isentropic Euler equations with the ideal gas law. He exhibits a set of smooth initial data that give rise to shock...
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High Order Structure-Preserving Finite Difference WENO Schemes for MHD Equations with Gravitation in all Sonic Mach Numbers
In this paper, we develop a high-order semi-implicit (SI) structure-preserving finite difference weighted essentially nonoscillatory (WENO) scheme...
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Existence, uniqueness and decay rates of a certain type of 3D Hall-MHD equations with power-law type
We investigate the local-in-time existence results of classical solutions to the 3D (Hall-)MHD equations with power-law type nonlinear viscous fluid...
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Stabilization Effects of Magnetic Field on a 2D Anisotropic MHD System with Partial Dissipation
To uncover that the magnetic field mechanism can stabilize electrically conducting turbulent fluids, we investigate the stability of a special two...
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The well posedness of solutions for the 2D magnetomicropolar boundary layer equations in an analytic framework
In this paper, we prove the existence and uniqueness of solutions to the 2D magnetomicropolar boundary layer equations on the half-plane by using the...
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A second-order scheme based on blended BDF for the incompressible MHD system
For the incompressible MHD equations, we present a fully discrete second-order-in-time scheme based on a blended BDF and extrapolation treatments for...
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Global Axisymmetric Solutions to the 3D MHD Equations with Nonzero Swirl
This paper studies sufficient conditions under which axisymmetric solutions with nonzero swirl components to the Cauchy problem of the 3D...
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Remarks on Liouville-Type Theorems for the Steady MHD and Hall-MHD Equations
In this note, we investigate Liouville-type theorems for the steady three-dimensional MHD and Hall-MHD equations and show that the velocity field u ...
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Well-Posedness in Gevrey Function Space for the 3D Axially Symmetric MHD Boundary Layer Equations Without Structural Assumption
In this paper, we establish the well-posedness theory for the three-dimensional axially symmetric magnetohydrodynamic (MHD) boundary layer system in...
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A High-Order Residual-Based Viscosity Finite Element Method for the Ideal MHD Equations
We present a high order, robust, and stable shock-capturing technique for finite element approximations of ideal MHD. The method uses continuous...
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Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows
In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with...