Finite-energy weak solutions to ideal MHD exist with time-varying magnetic helicity, proving they are not attainable in the infinite-conductivity zero-viscosity limit.
On turbulence and geometry: from Nash to Onsager
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abstract
This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric embeddings.
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Weak solutions of ideal MHD which do not conserve magnetic helicity
Finite-energy weak solutions to ideal MHD exist with time-varying magnetic helicity, proving they are not attainable in the infinite-conductivity zero-viscosity limit.