Anomalous dissipation of energy and magnetic helicity for the electron-MHD system
Mimi Dai, Han Liu
TL;DR
This paper uses convex integration to construct weak solutions to the electron-MHD system that violate energy and magnetic helicity conservation, highlighting anomalous dissipation phenomena.
Contribution
It introduces a novel application of convex integration to the electron-MHD system, demonstrating non-conservation of key physical quantities.
Findings
Weak solutions with anomalous dissipation constructed
Energy and magnetic helicity are not conserved in these solutions
Highlights limitations of classical conservation laws in electron-MHD
Abstract
Via convex integration, we construct weak solutions to the non-resistive electron-MHD system which do not conserve energy and magnetic helicity.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Navier-Stokes equation solutions · Gas Dynamics and Kinetic Theory