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

Hi Jun Choe, Hyunseok Kim

Research output: Contribution to journalArticle

86 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

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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