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Global regularity of the two-dimensional incompressible generalized magnetohydrodynamics system. (English) Zbl 1288.35406
It is shown that the generalized incompressible MHD equations – where the velocity dissipation exponent (of the Navier-Stokes member) is greater than or equal to $$\frac14$$ – admit a globally regular solution. (The word “generalized” here simply means that the authors consider the problem in a broader view where the Navier-Stokes member an the magnetic diffusion exponent may have values that differ from the usual ones in customary MHD).

MSC:
 35Q35 PDEs in connection with fluid mechanics 35B35 Stability in context of PDEs 35B65 Smoothness and regularity of solutions to PDEs 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 76W05 Magnetohydrodynamics and electrohydrodynamics
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