On the global regularity of two-dimensional generalized magnetohydrodynamics system

Abstract

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 $\beta =1$, in contrast to the previous result of $\alpha \ge \frac{1}{2}$, we show that $\alpha >\frac{1}{3}$ suffices in order for the solution pair to remain smooth for all time.

This is the version accepted by the Journal of Mathematical Analysis and Applications

References in corpus (5)

• The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations
• On the regularity of a class of generalized quasi-geostrophic equations
• A Remark on the Global Well-posedness of a Modified Critical Quasi-geostrophic Equation
• The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
• Remarks on global regularity of 2D generalized MHD equations

Cited by in corpus (3)

• The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion
• A remark on the two-dimensional magneto-hydrodynamics-alpha system
• Global small solution to the 2D MHD system with a velocity damping term