Kazuo Yamazaki
Published 2013-06-12, updated 2013-07-25Version 2
We study the two-dimensional generalized magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional Laplacians. It is known that the classical magnetohydrodynamics system with full Laplacians in both dissipation and diffusion terms admits a unique global strong solution pair. Making use of the special structure of the system in the two-dimensional case, we show in particular that the solution pair remains smooth when we have zero dissipation but only magnetic diffusion with its power of the fractional Laplacian $\beta > \frac{3}{2}$.
Comments: Some typos were fixed and details were added
Journal: Nonlinear Anal., 94 (2014) 194-205
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