This paper surveys recent developments on the global regularity and related problems on
the 2D incompressible magnetohydrodynamic (MHD) equations with partial or fractional …

Global existence and decay of smooth solution for the 2-D MHD equations without magnetic
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For highly coupled nonlinear incompressible magnetohydrodynamic (MHD) system, a well-
known numerical challenge is how to establish an unconditionally energy stable linearized …

This paper examines the global (in time) regularity of classical solutions to the two-
dimensional (2D) incompressible magnetohydrodynamics (MHD) equations with only …

This paper studies the Cauchy problem of the incompressible magnetohydro dynamic
systems with or without viscosity ν. Under the assumption that the initial velocity field and the …

In this paper, we propose and analyze a fully discrete finite element projection method for
the magnetohydrodynamic (MHD) equations. A modified Crank–Nicolson method and the …

This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with
mixed partial dissipation and magnetic diffusion. Our main result assesses the global …

This paper establishes the local-in-time existence and uniqueness of solutions to the
viscous, non-resistive magnetohydrodynamics (MHD) equations in R^ d R d, where d= 2, 3 …

Magnetohydrodynamics (MHD) studies the dynamics of magnetic fields in electrically
conducting fluids. In addition to the sound wave and electromagnetic wave behaviors …

In the short article we study the ideal incompressible magnetohydrodynamic equations in
three dimensions in which the Faraday law is inviscid. We prove the global well-posedness …