A Derivation of the Magnetohydrodynamic System from Navier–Stokes–Maxwell Systems

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We provide a full and rigorous derivation of the standard viscous magnetohydrodynamic system (MHD) as the asymptotic limit of Navier–Stokes–Maxwell systems when the speed of light is infinitely large. We work in the physical setting provided by the natural energy bounds and therefore mainly consider Leray solutions of fluid dynamical systems. Our methods are based on a direct analysis of frequencies and we are able to establish the weak stability of a crucial nonlinear term (the Lorentz force), neither assuming any strong compactness of the components nor applying standard compensated compactness methods (which actually fail in this case).

Original languageEnglish (US)
Pages (from-to)767-812
Number of pages46
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - Jun 1 2015

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


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