A new class of regularity criteria for the MHD and Navier-Stokes equations

In Skalak (0000) we studied a new class of the regularity criteria for the Navier- Stokes equations based on a remarkable idea that controlling the derivatives of some fundamental quantities like the pressure and the velocity along the streamlines yields the regularity of the weak solutions. We show in the present paper that the results from Skalak (0000) are extendable to the MHD equations and in the framework of the Besov spaces. For example, controlling the directional derivative of the magnetic Bernoulli pressure P along w+/|w+|, where w+ = u+b and u and b denote the velocity field and the magnetic field, respectively, yields the regularity. We compare our results with the similar criteria from the literature.(c) 2023 Elsevier Ltd. All rights reserved.