Weak Solutions of Ideal MHD Which Do Not Conserve Magnetic Helicity

Rajendra Beekie, Tristan Buckmaster, Vlad Vicol

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number1
JournalAnnals of PDE
Issue number1
StatePublished - Jun 1 2020

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Geometry and Topology
  • Mathematical Physics
  • General Physics and Astronomy


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