Local kinetic energy and singularities of the incompressible Navier–Stokes equations

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2 Citations (Scopus)

Abstract

We study the partial regularity problem of the incompressible Navier–Stokes equations. A reverse Hölder inequality of velocity gradient with increasing support is obtained under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions v belong to L(0,T;L3,w(R3)) where L3,w(R3) denotes the standard weak Lebesgue space.

Original languageEnglish
Pages (from-to)1171-1191
Number of pages21
JournalJournal of Differential Equations
Volume264
Issue number2
DOIs
Publication statusPublished - 2018 Jan 15

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Minkowski Dimension
Reverse Inequality
Incompressible Navier-Stokes
Partial Regularity
Singular Set
Lebesgue Space
Hausdorff Dimension
Kinetic energy
Weak Solution
Navier-Stokes Equations
Singularity
Gradient
Denote
Standards

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

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abstract = "We study the partial regularity problem of the incompressible Navier–Stokes equations. A reverse H{\"o}lder inequality of velocity gradient with increasing support is obtained under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded. As an application, we give a new bound for the Hausdorff dimension and the Minkowski dimension of singular set when weak solutions v belong to L∞(0,T;L3,w(R3)) where L3,w(R3) denotes the standard weak Lebesgue space.",
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Local kinetic energy and singularities of the incompressible Navier–Stokes equations. / Choe, Hi Jun; Yang, Minsuk.

In: Journal of Differential Equations, Vol. 264, No. 2, 15.01.2018, p. 1171-1191.

Research output: Contribution to journalArticle

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