Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations

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Abstract

We derive a local energy inequality for weak solutions of the three dimensional magnetohydrodynamic equations. Combining Biot–Savart law, interpolation inequalities and the local energy inequality, we prove a partial regularity theorem for suitable weak solutions. Furthermore, we obtain an improved estimate for the logarithmic Hausdorff dimension of the singular set of suitable weak solutions.

Original languageEnglish
Pages (from-to)171-198
Number of pages28
JournalCommunications in Mathematical Physics
Volume336
Issue number1
DOIs
Publication statusPublished - 2015 Jan 1

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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