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Weak solutions of ideal MHD which do not conserve magnetic helicity

PDE and Applied Math Seminar

Speaker: Vlad Vicol, Courant, NYU
Location: 2112 MSB
Start time: Thu, Oct 24 2019, 4:30PM

We construct weak solutions to the ideal magneto-hydrodynamic (MHD) equations which have finite total energy, and whose magnetic helicity is not a constant function of time. In view of Taylor’s conjecture, this proves that there exist finite energy weak solutions to ideal MHD which cannot be attained in the infinite conductivity and zero viscosity limit. Our proof is based on a Nash-type convex integration scheme with intermittent building blocks adapted to the geometry of the MHD system. This is joint work with R. Beekie and T. Buckmaster.