# Mathematics Colloquia and Seminars

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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 Taylorâ€™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.