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Regular version of the site

Article

A generalization of the arnol'd inequality in MHD

Magnetohydrodynamics. 2016. Vol. 52. No. 1. P. 5-14.
Akhmet’ev P., Kudryavtseva E., Smirnov A.

The Arnol'd inequality estimates the magnetic energy U^{(2)}(B) = ∫_Ω (B,B) dR^3 from below by means of the magnetic helicity χ(B) = ∫_Ω (A,B) dR^3. A new modification of the Arnol'd inequality is proved using the magnetic U^{(4)}-energy and the magnetic quadratic helicity χ^{(2)}.