On regularity and singularity for L∞(0 , T; L3                             ,                             w(R3)) solutions to the Navier–Stokes equations

Hi Jun Choe; Jörg Wolf; Minsuk Yang

doi:10.1007/s00208-019-01843-2

On regularity and singularity for L^∞(0 , T; L³ ^, ^w(R³)) solutions to the Navier–Stokes equations

Hi Jun Choe, Jörg Wolf, Minsuk Yang

Department of Mathematics

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

6 Citations (Scopus)

Abstract

We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier–Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L^∞(0 , T; L³ ^, ^w(R³)) without any smallness assumption on that scale, where L³ ^, ^w(R³) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t.

Original language	English
Pages (from-to)	617-642
Number of pages	26
Journal	Mathematische Annalen
Volume	377
Issue number	1-2
DOIs	https://doi.org/10.1007/s00208-019-01843-2
Publication status	Published - 2020 Jun 1

Bibliographical note

Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s00208-019-01843-2

Cite this

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abstract = "We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier–Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L∞(0 , T; L3 , w(R3)) without any smallness assumption on that scale, where L3 , w(R3) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t.",

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AU - Wolf, Jörg

AU - Yang, Minsuk

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N2 - We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier–Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L∞(0 , T; L3 , w(R3)) without any smallness assumption on that scale, where L3 , w(R3) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t.

AB - We study local regularity properties of a weak solution u to the Cauchy problem of the incompressible Navier–Stokes equations. We present a new regularity criterion for the weak solution u satisfying the condition L∞(0 , T; L3 , w(R3)) without any smallness assumption on that scale, where L3 , w(R3) denotes the standard weak Lebesgue space. As an application, we conclude that there are at most a finite number of blowup points at any singular time t.

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