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Journal of Mathematical Fluid Mechanics

, Volume 12, Issue 4, pp 536–553 | Cite as

Asymptotic Properties of Solutions to the Equations of Incompressible Fluid Mechanics

  • Jan BřezinaEmail author
Article

Abstract.

Well-accepted hypothesis in the fluid dynamics is that if the boundary of the physical domain is impermeable then the viscous fluid adheres completely to it. Many authors recently proposed mathematical justifications for this hypothesis using the so-called rugous boundary. In this Paper we want to discuss optimality of results obtained in Bucur et al. [3], Bucur and Feireisl [4] or Díaz et al. [5] and we show several corresponding examples. Finally, we extend these results for more general domains.

Mathematics Subject Classification (2000).

35G30 

Keywords.

Navier–Stokes equations boundary conditions rough boundary 

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Copyright information

© Birkhäuser Verlag, Basel 2009

Authors and Affiliations

  1. 1.Mathematical Institute of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic

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