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On the asymptotic limit of the Navier-Stokes system on domains with rough boundaries |
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| Authors: | Dorin Bucur Eduard Feireisl Šárka Ne?asová Joerg Wolf |
| Institution: | a Département de Mathématiques, Université de Metz, Ile de Saulcy, 57045 Metz Cedex, France b Mathematical Institute of the Academy of Sciences of the Czech Republic, ?itná 25, 115 67 Praha 1, Czech Republic c Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chausse 25, 12489 Berlin, Germany |
| Abstract: | 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 are non-degenerate, meaning not oriented in a single direction. |
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