A note on regularity conditions on ideal magnetohydrodynamic equations

Note on solution regularity of the generalized magnetohydrodynamic equations with partial dissipation

On global regularity of 2D generalized magnetohydrodynamic equations

A note on permutation regularity

A note on permutation regularity

Global Regularity for a Class of Generalized Magnetohydrodynamic Equations

It remains unknown whether or not smooth solutions of the 3D incompressible MHD equations can develop finite-time singularities. One major difficulty is due to the fact that the dissipation given by the Laplacian operator is insufficient to control the nonlinearity and for this reason the 3D MHD equations are sometimes regarded as “supercritical”. This paper presents a global regularity result ...

A Constrained-Transport E-CUSP scheme for Ideal Magnetohydrodynamic Equations

The constrained transport algorithm combined with an E-CUSP scheme is developed to solve the ideal magnetohydrodynamic equations. The algorithm can preserve the divergence-free condition for the magnetic field and maintain the advantages of simplicity and low diffusion of the E-CUSP scheme. The numerical results demonstrate the robustness and efficiency of this new algorithm.