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Wall laws for fluid flows at a boundary with random roughness. (English) Zbl 1179.35207
It is a very interesting paper, concerning the effects of roughness-walls in fluid dynamics. The problem is to derive some wall laws, describing the macroscopic effect of the micro-structures related with non-smooth boundaries. As difference with many previous papers, here the roughness is described by a spatially homogeneous random field (related with a small parameter) and not by periodic structures. The point is to study the limit process when the small parameter tends to zero. The analysis is limited to the case of a small flux of a Navier-Stokes fluid in a channel type domain. The difficulties related with the unbounded domains are overcome by deriving new energy estimates. The ergodic theorem is used to specify the behaviour of the solution far from boundaries. The authors obtain the Navier wall law in a rigorous way, improving the previous results. A large list of references is given in the last part.

MSC:
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
60H30 Applications of stochastic analysis (to PDEs, etc.)
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