Global regularity of the two-dimensional incompressible generalized magnetohydrodynamics system

In this paper, we consider the global regularity of the two-dimensional generalized incompressible magnetohydrodynamics system with velocity dissipation exponent α≥14 and magnetic diffusion exponent β=1β=1 based on the improved integrability in terms of vorticity. This result is a further improvement of very recent works (Jiu and Zhao (2014) and Yamazaki (2013)) which require α>13 and β=1β=1. Therefore our result is more closer to the resolution of the well-known global regularity issue on the 2D magnetohydrodynamics system α=0,β=1.