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On Partial Regularity for the Steady Hall Magnetohydrodynamics System

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Abstract

We study partial regularity of suitable weak solutions of the steady Hall magnetohydrodynamics equations in a domain \({\Omega \subset \mathbb{R}^3}\). In particular, we prove that the set of possible singularities of the suitable weak solution has Hausdorff dimension at most one. Moreover, in the case \({\Omega=\mathbb{R}^3}\), we show that the set of possible singularities is compact.

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Authors and Affiliations

  1. Department of Mathematics, Chung-Ang University, Seoul, 156-756, Republic of Korea

    Dongho Chae

  2. Department of Financial Engineering, Ajou University, Suwon, 443-749, Republic of Korea

    Jörg Wolf

Authors
  1. Dongho Chae
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  2. Jörg Wolf
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Correspondence to Dongho Chae.

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Communicated by L. Caffarelli

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Chae, D., Wolf, J. On Partial Regularity for the Steady Hall Magnetohydrodynamics System. Commun. Math. Phys. 339, 1147–1166 (2015). https://doi.org/10.1007/s00220-015-2429-2

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  • DOI: https://doi.org/10.1007/s00220-015-2429-2

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