Global mild solutions of Navier-Stokes equations

Zhen Lei, Fang-Hua Lin

Research output: Contribution to journalArticle

Abstract

We establish a global well-posedness of mild solutions to the three-dimensional, incompressible Navier-Stokes equations if the initial data are in the space χ -1 defined by χ -1 = {f ∈ D' (R 3): R 3 |ξ| -1|f̂|d ξ ≤ ∞}and if the norms of the initial data in χ -1 are bounded exactly by the viscosity coefficient μ.

Original languageEnglish (US)
Pages (from-to)1297-1304
Number of pages8
JournalCommunications on Pure and Applied Mathematics
Volume64
Issue number9
DOIs
StatePublished - Sep 2011

Fingerprint

Mild Solution
Navier Stokes equations
Navier-Stokes Equations
Viscosity
Global Well-posedness
Incompressible Navier-Stokes Equations
Research and Development
Norm
Three-dimensional
Coefficient

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Global mild solutions of Navier-Stokes equations. / Lei, Zhen; Lin, Fang-Hua.

In: Communications on Pure and Applied Mathematics, Vol. 64, No. 9, 09.2011, p. 1297-1304.

Research output: Contribution to journalArticle

@article{6e14348daaa84ce583e58feb863e7162,
title = "Global mild solutions of Navier-Stokes equations",
abstract = "We establish a global well-posedness of mild solutions to the three-dimensional, incompressible Navier-Stokes equations if the initial data are in the space χ -1 defined by χ -1 = {f ∈ D' (R 3): R 3 |ξ| -1|f̂|d ξ ≤ ∞}and if the norms of the initial data in χ -1 are bounded exactly by the viscosity coefficient μ.",
author = "Zhen Lei and Fang-Hua Lin",
year = "2011",
month = "9",
doi = "10.1002/cpa.20361",
language = "English (US)",
volume = "64",
pages = "1297--1304",
journal = "Communications on Pure and Applied Mathematics",
issn = "0010-3640",
publisher = "Wiley-Liss Inc.",
number = "9",

}

TY - JOUR

T1 - Global mild solutions of Navier-Stokes equations

AU - Lei, Zhen

AU - Lin, Fang-Hua

PY - 2011/9

Y1 - 2011/9

N2 - We establish a global well-posedness of mild solutions to the three-dimensional, incompressible Navier-Stokes equations if the initial data are in the space χ -1 defined by χ -1 = {f ∈ D' (R 3): R 3 |ξ| -1|f̂|d ξ ≤ ∞}and if the norms of the initial data in χ -1 are bounded exactly by the viscosity coefficient μ.

AB - We establish a global well-posedness of mild solutions to the three-dimensional, incompressible Navier-Stokes equations if the initial data are in the space χ -1 defined by χ -1 = {f ∈ D' (R 3): R 3 |ξ| -1|f̂|d ξ ≤ ∞}and if the norms of the initial data in χ -1 are bounded exactly by the viscosity coefficient μ.

UR - http://www.scopus.com/inward/record.url?scp=79957784205&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957784205&partnerID=8YFLogxK

U2 - 10.1002/cpa.20361

DO - 10.1002/cpa.20361

M3 - Article

AN - SCOPUS:79957784205

VL - 64

SP - 1297

EP - 1304

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 9

ER -