On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces

Abstract

We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to experience a finite-time blowup. Following the work of [12] and making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one of the three components of the velocity vector field, both in scaling-invariant spaces.

This is the version accepted by Bull. Sci. Math., currently in press. There is no mathematical change at all, only grammatical and formatting revision, Bull. Sci. Math. (2015)

References in corpus (2)

• Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor
• On well-posedness of the Cauchy problem for MHD system in Besov spaces

Cited by in corpus (1)

• Regularity criteria for the Kuramoto-Sivashinsky equation in dimensions two and three