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.
The Onsager conjecture in 2D: a Newton–Nash iteration.Inventiones Mathematicae, 238(2):691–768, 2024
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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.