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manuscripta mathematica

, Volume 120, Issue 1, pp 91–129 | Cite as

On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities

  • Yonggeun ChoEmail author
  • Hyunseok Kim
Article

Abstract

We study the Navier-Stokes equations for compressible barotropic fluids in a bounded or unbounded domain Ω of R 3. We first prove the local existence of solutions (ρ,u) in C([0,T*]; (ρ +H 3(Ω)) × Open image in new window under the assumption that the data satisfies a natural compatibility condition. Then deriving the smoothing effect of the velocity u in t>0, we conclude that (ρ,u) is a classical solution in (0,T **)×Ω for some T ** ∈ (0,T *]. For these results, the initial density needs not be bounded below away from zero and may vanish in an open subset (vacuum) of Ω.

Mathematics Subject Classification (2000)

35Q30 76N10 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of MathematicsHokkaido UniversitySapporoJapan
  2. 2.Department of MathematicsSogang UniversitySeoulKorea

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