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Journal of Mathematical Fluid Mechanics

, Volume 13, Issue 2, pp 173–189 | Cite as

Singular Limits of the Equations of Magnetohydrodynamics

  • Peter KukučkaEmail author
Article

Abstract

This paper studies the asymptotic limit for solutions to the equations of magnetohydrodynamics, specifically, the Navier–Stokes–Fourier system describing the evolution of a compressible, viscous, and heat conducting fluid coupled with the Maxwell equations governing the behavior of the magnetic field, when Mach number and Alfvén number tends to zero. The introduced system is considered on a bounded spatial domain in \({\mathbb{R}^{3}}\), supplemented with conservative boundary conditions. Convergence towards the incompressible system of the equations of magnetohydrodynamics is shown.

Mathematics Subject Classification (2000)

35A05 35Q30 35Q60 

Keywords

Navier–Stokes–Fourier system Oberbeck-Boussinesq approximation Maxwell equations 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Mathematical Institute of the ASCRPraha 1Czech Republic

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