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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Y. Shibata
This work was supported by Grant 201/08/0315 of GA ČR in the framework of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.
Rights and permissions
About this article
Cite this article
Březina, J. Asymptotic Properties of Solutions to the Equations of Incompressible Fluid Mechanics. J. Math. Fluid Mech. 12, 536–553 (2010). https://doi.org/10.1007/s00021-009-0301-x
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00021-009-0301-x