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Global Low-Energy Weak Solutions of the Equations of Three-Dimensional Compressible Magnetohydrodynamics

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Abstract

We prove the global-in-time existence of weak solutions of the equations of compressible magnetohydrodynamics in three space dimensions with initial data small in L 2 and initial density positive and essentially bounded. A great deal of information concerning partial regularity is obtained: velocity, vorticity, and magnetic field become relatively smooth in positive time (H 1 but not H 2) and singularities in the pressure cancel those in a certain multiple of the divergence of the velocity, thus giving concrete expression to conclusions obtained formally from the Rankine–Hugoniot conditions.

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Authors and Affiliations

  1. Department of Mathematics, Indiana University, Bloomington, IN, 47405, USA

    Anthony Suen & David Hoff

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  1. Anthony Suen
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  2. David Hoff
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Correspondence to Anthony Suen.

Additional information

Communicated by S. Müller

This research was supported in part by the NSF under Grant DMS-0758043.

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Suen, A., Hoff, D. Global Low-Energy Weak Solutions of the Equations of Three-Dimensional Compressible Magnetohydrodynamics. Arch Rational Mech Anal 205, 27–58 (2012). https://doi.org/10.1007/s00205-012-0498-3

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  • DOI: https://doi.org/10.1007/s00205-012-0498-3

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