Asymptotic Properties of Solutions to the Equations of Incompressible Fluid Mechanics
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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. , Bucur and Feireisl  or Díaz et al.  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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