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

Research output: Contribution to journalArticle

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 languageEnglish
JournalMathematische Annalen
DOIs
Publication statusPublished - 2019 Jan 1

Fingerprint

Weak Solution
Navier-Stokes Equations
Regularity
Singularity
Incompressible Navier-Stokes
Regularity Criterion
Lebesgue Space
Regularity Properties
Local Properties
Blow-up
Cauchy Problem
Denote
Standards

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{ec9bd19a0859442a9458cc8b364ca9e2,
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.",
author = "Choe, {Hi Jun} and J{\"o}rg Wolf and Minsuk Yang",
year = "2019",
month = "1",
day = "1",
doi = "10.1007/s00208-019-01843-2",
language = "English",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",

}

TY - JOUR

T1 - On regularity and singularity for L∞(0 , T; L3,w(R3)) solutions to the Navier–Stokes equations

AU - Choe, Hi Jun

AU - Wolf, Jörg

AU - Yang, Minsuk

PY - 2019/1/1

Y1 - 2019/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85066102034&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066102034&partnerID=8YFLogxK

U2 - 10.1007/s00208-019-01843-2

DO - 10.1007/s00208-019-01843-2

M3 - Article

AN - SCOPUS:85066102034

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

ER -