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Inventiones mathematicae

, Volume 141, Issue 3, pp 579–614 | Cite as

Global existence in critical spaces for compressible Navier-Stokes equations

  • R. Danchin

Abstract.

We investigate global strong solutions for isentropic compressible fluids with initial data close to a stable equilibrium. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated equations. More precisely, the initial velocity has the same critical regularity index as for the incompressible homogeneous Navier-Stokes equations, and one more derivative is needed for the density. We point out a smoothing effect on the velocity and a L 1-decay on the difference between the density and the constant reference state. The proof lies on uniform estimates for a mixed hyperbolic/parabolic linear system with a convection term.

Keywords

Convection Linear System Initial Data Reference State Initial Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • R. Danchin
    • 1
  1. 1.Laboratoire d’Analyse Numérique, Université Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, FranceFR

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