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In this paper, we derive the optimal boundary conditions of the Navier-Stokes fluid in a bounded domain with a thin layer. We get the effects of the layer by investigating the limiting δ, the thickness of the layer shrinking to zero. In the two-dimensional case, we derive effective boundary conditions by the limit of u and p on the boundary of the uncoated body.

Optimal boundary conditions for the Navier-Stokes fluid in a bounded domain with a thin layer