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

Hi Jun Choe; Hyunseok Kim

doi:10.1081/pde-120021191

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

Hi Jun Choe, Hyunseok Kim

Department of Mathematics

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

147 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 language	English
Pages (from-to)	1183-1201
Number of pages	19
Journal	Communications in Partial Differential Equations
Volume	28
Issue number	5-6
DOIs	https://doi.org/10.1081/pde-120021191
Publication status	Published - 2003

Bibliographical note

Funding Information:
The first author was supported by KRF and KOSEF. The second author was supported by Com2Mac-KOSEF.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1081/pde-120021191

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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",

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

AU - Choe, Hi Jun

AU - Kim, Hyunseok

N1 - Funding Information: The first author was supported by KRF and KOSEF. The second author was supported by Com2Mac-KOSEF.

PY - 2003

Y1 - 2003

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.

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EP - 1201

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 5-6

ER -

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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