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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer Berlin Heidelberg

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DOI

10.1007/s007060170141

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1432-0916

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On the Weak Solutions to the Maxwell–Landau–Lifshi

Authors: Eric Dumas Franck Sueur
Publish Date: 2014/03/14
Volume: 330, Issue: 3, Pages: 1179-1225
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Abstract

In this paper we deal with weak solutions to the Maxwell–Landau–Lifshitz equations and to the Hall–Magneto–Hydrodynamic equations First we prove that these solutions satisfy some weakstrong uniqueness property Then we investigate the validity of energy identities In particular we give a sufficient condition on the regularity of weak solutions to rule out anomalous dissipation In the case of the Hall–Magneto–Hydrodynamic equations we also give a sufficient condition to guarantee the magnetohelicity identity Our conditions correspond to the same heuristic scaling as the one introduced by Onsager in hydrodynamic theory Finally we examine the sign locally of the anomalous dissipations of weak solutions obtained by some natural approximation processes

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