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The Dirichlet Problems for Steady Navier-Stokes Equations in Domains with Thin Channels

In: Advances in Mathematical Fluid Mechanics

Author

Listed:
  • Yu V. Namlyeyeva

    (Institute of Applied Mathematics and Mechanics of NAS of Ukraine)

  • Š Nečcasová

    (Mathematical Institute of Academy of Sciences)

  • I.I. Skrypnik

    (Institute of Applied Mathematics and Mechanics of NAS of Ukraine)

Abstract

We consider a sequence of the Dirichlet problems for steady Navier- Stokes equations in domains perforated with channels where are closed subsets of bounded domain containedin small neighborhoods of some lines. While the number I (s) of channels tends toinfinity as these small sets are thinned.We study the asymptotic behaviorof solutions us (x) to problems in domains with thin channels. Wefind conditions on perforated domains under which sequence of solutions converges to solution of homogenized problem as. The proof is based on the asymptotic expansion of us (x) and on pointwise and integral estimates of auxiliary functions which are solutions of model boundary value problems.

Suggested Citation

  • Yu V. Namlyeyeva & Š Nečcasová & I.I. Skrypnik, 2010. "The Dirichlet Problems for Steady Navier-Stokes Equations in Domains with Thin Channels," Springer Books, in: Rolf Rannacher & Adélia Sequeira (ed.), Advances in Mathematical Fluid Mechanics, pages 339-366, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04068-9_22
    DOI: 10.1007/978-3-642-04068-9_22
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