Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations

Hi Jun Choe; Minsuk Yang

doi:10.1007/s00220-015-2307-y

Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations

Hi Jun Choe, Minsuk Yang

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

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 language	English
Pages (from-to)	171-198
Number of pages	28
Journal	Communications in Mathematical Physics
Volume	336
Issue number	1
DOIs	https://doi.org/10.1007/s00220-015-2307-y
Publication status	Published - 2015 May

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Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-015-2307-y

Cite this

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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.",

author = "Choe, {Hi Jun} and Minsuk Yang",

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AB - 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.

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Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations

Abstract

Bibliographical note

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