Differential and Integral Equations

Remarks on a nonhomogeneous model of magnetohydrodynamics

B. Desjardins and C. Le Bris

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Abstract

This paper is devoted to a model of magnetohydrodynamics described by a parabolic system of partial differential equations coupling the nonhomogeneous incompressible Navier--Stokes equations and Maxwell's equations. In the case of two-dimensional flows, we prove global regularity results under the assumption that the fluids' viscosities are close enough to their average. On the other hand, a more detailed description of the interface and of the regularity of the third component of the magnetic field is given when the fluids have the same viscosity.

Article information

Source
Differential Integral Equations, Volume 11, Number 3 (1998), 377-394.

Dates
First available in Project Euclid: 30 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367341058

Mathematical Reviews number (MathSciNet)
MR1745545

Zentralblatt MATH identifier
1067.76097

Subjects
Primary: 76W05: Magnetohydrodynamics and electrohydrodynamics
Secondary: 35Q60: PDEs in connection with optics and electromagnetic theory

Citation

Desjardins, B.; Le Bris, C. Remarks on a nonhomogeneous model of magnetohydrodynamics. Differential Integral Equations 11 (1998), no. 3, 377--394. https://projecteuclid.org/euclid.die/1367341058


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