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On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries. (English) Zbl 1143.35080
Summary: We study the asymptotic behavior of solutions to the incompressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations to be non-degenerate, i.e. not oriented in a single direction.

MSC:
35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
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