Limiting case for the regularity criterion to the 3-D Magneto-hydrodynamics equations

Abstract

We prove that any weak solution (u,b) of three-dimensional incompressible Magneto-hydrodynamics equations is regular if u∈L∞(0,T;L3(R3)) and b∈L∞(0,T;VMO−1(R3)). The proof is based on the blow-up analysis and backward uniqueness for the parabolic operator developed by Escauriaza–Seregin–Šverák.