A New Regularity Criterion for the Three-Dimensional Incompressible Magnetohydrodynamic Equations in the Besov Spaces

Regularity criteria of the weak solutions to the three-dimensional (3D) incompressible magnetohydrodynamic (MHD) equations are discussed. Our results imply that the scalar pressure field pi plays an important role in the regularity problem of MHD equations. We derive that the weak solution (u, b) is regular on (0, T], which is provided for the scalar pressure field pi in the Besov spaces.

Automated summary

The regularity criteria of the weak solutions to the 3D incompressible MHD equations are discussed, highlighting the importance of the scalar pressure field. It is shown that the weak solution is regular over a specific time interval in the Besov spaces.