Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids

Hi Jun Choe, Hyunseok Kim

Research output: Contribution to journalArticle

79 Citations (Scopus)

Abstract

We study strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R3. Deriving higher a priori estimates independent of the lower bounds of the density, we prove the existence and uniqueness of local strong solutions to the initial value problem (for Ω = R3) or the initial boundary value problem (for Ω ⊂ ⊂ R3) even though the initial density vanishes in an open subset of Ω, i.e., an initial vacuum exists. As an immediate consequence of the a priori estimates, we obtain a continuation theorem for the local strong solutions.

Original languageEnglish
Pages (from-to)1183-1201
Number of pages19
JournalCommunications in Partial Differential Equations
Volume28
Issue number5-6
Publication statusPublished - 2003 Jan 1

Fingerprint

Strong Solution
Incompressible Fluid
Navier Stokes equations
Navier-Stokes Equations
A Priori Estimates
Fluids
Initial value problems
Boundary value problems
Continuation Theorem
Vacuum
Initial-boundary-value Problem
Initial Value Problem
Vanish
Existence and Uniqueness
Lower bound
Subset

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Analysis
  • Applied Mathematics

Cite this

@article{9a82148f1ee845a69424167c2fb35c00,
title = "Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids",
abstract = "We study strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R3. Deriving higher a priori estimates independent of the lower bounds of the density, we prove the existence and uniqueness of local strong solutions to the initial value problem (for Ω = R3) or the initial boundary value problem (for Ω ⊂ ⊂ R3) even though the initial density vanishes in an open subset of Ω, i.e., an initial vacuum exists. As an immediate consequence of the a priori estimates, we obtain a continuation theorem for the local strong solutions.",
author = "Choe, {Hi Jun} and Hyunseok Kim",
year = "2003",
month = "1",
day = "1",
language = "English",
volume = "28",
pages = "1183--1201",
journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor and Francis Ltd.",
number = "5-6",

}

Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids. / Choe, Hi Jun; Kim, Hyunseok.

In: Communications in Partial Differential Equations, Vol. 28, No. 5-6, 01.01.2003, p. 1183-1201.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids

AU - Choe, Hi Jun

AU - Kim, Hyunseok

PY - 2003/1/1

Y1 - 2003/1/1

N2 - We study strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R3. Deriving higher a priori estimates independent of the lower bounds of the density, we prove the existence and uniqueness of local strong solutions to the initial value problem (for Ω = R3) or the initial boundary value problem (for Ω ⊂ ⊂ R3) even though the initial density vanishes in an open subset of Ω, i.e., an initial vacuum exists. As an immediate consequence of the a priori estimates, we obtain a continuation theorem for the local strong solutions.

AB - We study strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R3. Deriving higher a priori estimates independent of the lower bounds of the density, we prove the existence and uniqueness of local strong solutions to the initial value problem (for Ω = R3) or the initial boundary value problem (for Ω ⊂ ⊂ R3) even though the initial density vanishes in an open subset of Ω, i.e., an initial vacuum exists. As an immediate consequence of the a priori estimates, we obtain a continuation theorem for the local strong solutions.

UR - http://www.scopus.com/inward/record.url?scp=0037704906&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0037704906&partnerID=8YFLogxK

M3 - Article

VL - 28

SP - 1183

EP - 1201

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

IS - 5-6

ER -