Journal of Mathematical Fluid Mechanics

, Volume 16, Issue 3, pp 571–594 | Cite as

Compressible Navier–Stokes Equations on Thin Domains

  • David MalteseEmail author
  • Antonín Novotný


We consider the barotropic Navier–Stokes system describing the motion of a compressible viscous fluid confined to a straight layer \({\Omega_\varepsilon = \omega\times (0, \varepsilon)}\) , where ω is a particular 2-D domain (a periodic cell, bounded domain or the whole 2-D space). We show that the weak solutions in the 3D domain converge to a (strong) solutions of the 2-D Navier–Stokes system on ω as \({\varepsilon \to 0}\) on the maximal life time of the strong solution.


Compressible Navier–Stokes system dimension reduction thin domains 


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© Springer Basel 2014

Authors and Affiliations

  1. 1.IMATH, EA 2134Université du Sud Toulon-VarLa GardeFrance

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