On the global regularity of two-dimensional generalized magnetohydrodynamics system

We study the two-dimensional generalized magnetohydrodynamics system with dissipation and diffusion in terms of fractional Laplacians. In particular, we show that in case the diffusion term has the power $β= 1$, in contrast to the previous result of $α\geq \frac{1}{2}$, we show that $α> \frac{1}{3}$ suffices in order for the solution pair to remain smooth for all time.

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