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

HANDLE Open Access

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)) × D^1_0 ∩ D^3)(Ω)) 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.

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Details 詳細情報について

  • CRID
    1050845763909243008
  • NII Article ID
    120000954460
  • ISSN
    14321785
    00252611
  • HANDLE
    2115/14421
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • IRDB
    • CiNii Articles

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