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

4 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

Funding Information:
H. J. Choe has been supported by the National Reserch Foundation of Korea (NRF) grant, funded by the Korea government(MSIP) (No. 2015R1A5A1009350). J. Wolf has been supported by the German Research Foundation (DFG) through the project WO1988/1-1; 612414. M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2015R1A5A1009350) and (No. 2016R1C1B2015731).

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

All Science Journal Classification (ASJC) codes

Mathematics(all)

Access to Document

10.1007/s00208-019-01843-2

Cite this

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

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 - Choe, Hi Jun

AU - Wolf, Jörg

AU - Yang, Minsuk

N1 - Funding Information: H. J. Choe has been supported by the National Reserch Foundation of Korea (NRF) grant, funded by the Korea government(MSIP) (No. 2015R1A5A1009350). J. Wolf has been supported by the German Research Foundation (DFG) through the project WO1988/1-1; 612414. M. Yang has been supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government(MSIP) (No. 2015R1A5A1009350) and (No. 2016R1C1B2015731). Publisher Copyright: © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

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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.

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