Weak solutions to ideal MHD on the 3-torus are constructed in C^γ for γ < 1/5 that do not conserve kinetic energy or cross-helicity via convex integration and Lie-algebra geometry.
Non-uniqueness and h-principle for H¨ older-continuous weak solutions of the Euler equa- tions.Archive for Rational Mechanics and Analysis, 224(2):471–514, February 2017
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$C^{1/5^{-}}$ Convex Integration Solutions of Ideal MHD
Weak solutions to ideal MHD on the 3-torus are constructed in C^γ for γ < 1/5 that do not conserve kinetic energy or cross-helicity via convex integration and Lie-algebra geometry.