Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations

Research output: Contribution to journalArticle

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

Fingerprint

Suitable Weak Solutions
Energy Inequality
Magnetohydrodynamic Equations
Singular Set
Hausdorff Measure
magnetohydrodynamics
Interpolation Inequality
Partial Regularity
Hausdorff Dimension
Weak Solution
Logarithmic
regularity
Three-dimensional
interpolation
theorems
Theorem
Estimate
energy
estimates

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

@article{60eefb46d98b4fdb8adcdf0481a18a4a,
title = "Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations",
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",
year = "2015",
month = "1",
day = "1",
doi = "10.1007/s00220-015-2307-y",
language = "English",
volume = "336",
pages = "171--198",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer New York",
number = "1",

}

Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations. / Choe, Hi Jun; Yang, Minsuk.

In: Communications in Mathematical Physics, Vol. 336, No. 1, 01.01.2015, p. 171-198.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations

AU - Choe, Hi Jun

AU - Yang, Minsuk

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84925541292&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925541292&partnerID=8YFLogxK

U2 - 10.1007/s00220-015-2307-y

DO - 10.1007/s00220-015-2307-y

M3 - Article

AN - SCOPUS:84925541292

VL - 336

SP - 171

EP - 198

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -