Global regularity of logarithmically supercritical 3-D LAMHD-alpha system with zero diffusion

We study the three-dimensional Lagrangian-averaged magnetohydrodynamics-alpha system with zero diffusion. Despite the dissipation strength at the logarithmically supercritical level, using dyadic decomposition techniques we show that given initial data sufficiently smooth, the solution pair remains smooth for all time. This settles the global regularity case suggested by the authors in [27].