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Some remarks on the boundary conditions in the theory of Navier-Stokes equations. (English. French summary) Zbl 1293.35232

Summary: This article addresses some theoretical questions related to the choice of boundary conditions, which are essential for modelling and numerical computing in mathematical fluids mechanics. Unlike the standard choice of the well known non slip boundary conditions, we emphasize three selected sets of slip conditions, and particularly stress on the interaction between the appropriate functional setting and the status of these conditions.

MSC:

35Q35 PDEs in connection with fluid mechanics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
76D05 Navier-Stokes equations for incompressible viscous fluids
35D30 Weak solutions to PDEs
76D07 Stokes and related (Oseen, etc.) flows
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