Low Regularity Regularity Global Solutions for a generalized MHD-alpha system

摘要

The Magneto-Hydrodynamic (MHD) system of equations governs the motion of viscous fluids subject to a magnetic field. Due to the difficulty of obtaining global solutions to the MHD system, it has become common to study modified versions of the system. In this paper, we prove the existence of a unique global solution to the incompressible MHD-alpha system with diffusion terms which are Fourier multipliers with symbols of the form m(xi) = vertical bar xi vertical bar(gamma)/g(vertical bar xi vertical bar)for gamma > 0 and g (essentially) a logarithm. Letting gamma(1). and gamma(2) be the regularity of the diffusion terms, we obtain global existence when gamma(1) and gamma(2) satisfy gamma(1), gamma(2) > 1, gamma(1) >= n/3, and gamma(1) + gamma(2) >= n in R-n for n >= 3. (C) 2017 Elsevier Ltd. All rights reserved.