### Abstract

We study strong solutions of the Navier-Stokes equations for nonhomogeneous incompressible fluids in Ω ⊂ R^{3}. 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 = R^{3}) or the initial boundary value problem (for Ω ⊂ ⊂ R^{3}) 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 |
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Pages (from-to) | 1183-1201 |

Number of pages | 19 |

Journal | Communications in Partial Differential Equations |

Volume | 28 |

Issue number | 5-6 |

Publication status | Published - 2003 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Analysis
- Applied Mathematics

### Cite this

*Communications in Partial Differential Equations*,

*28*(5-6), 1183-1201.

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*Communications in Partial Differential Equations*, vol. 28, no. 5-6, pp. 1183-1201.

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

Research output: Contribution to journal › Article

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 -