Unique solvability of the initial boundary value problems for compressible viscous fluids

Yonggeun Cho, Hi Jun Choe, Hyunseok Kim

Research output: Contribution to journalArticle

186 Citations (Scopus)

Abstract

We study the Navier-Stokes equations for compressible barotropic fluids in a domain Ω⊂ℝ3. We first prove the local existence of the unique strong solution, provided the initial data satisfy a natural compatibility condition. The initial density needs not be bounded away from zero; it may vanish in an open subset (vacuum) of Ω or decay at infinity when Ω is unbounded. We also prove a blow-up criterion for the local strong solution, which is new even for the case of positive initial densities. Finally, we prove that if the initial vacuum is not so irregular, then the compatibility condition of the initial data is necessary and sufficient to guarantee the existence of a unique strong solution.

Original languageEnglish
Pages (from-to)243-275
Number of pages33
JournalJournal des Mathematiques Pures et Appliquees
Volume83
Issue number2
DOIs
Publication statusPublished - 2004 Feb 1

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Unique Solvability
Compressible Fluid
Strong Solution
Viscous Fluid
Initial-boundary-value Problem
Boundary value problems
Compatibility Conditions
Vacuum
Fluids
Navier Stokes equations
Blow-up Criterion
Local Existence
Irregular
Vanish
Navier-Stokes Equations
Infinity
Decay
Sufficient
Subset
Necessary

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Unique solvability of the initial boundary value problems for compressible viscous fluids. / Cho, Yonggeun; Choe, Hi Jun; Kim, Hyunseok.

In: Journal des Mathematiques Pures et Appliquees, Vol. 83, No. 2, 01.02.2004, p. 243-275.

Research output: Contribution to journalArticle

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