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Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle. (English) Zbl 1205.35191
Summary: We analyze the spatial anisotropic profiles at infinity of steady Stokes and Navier-Stokes flows around a rotating obstacle. It is shown that the Stokes flow is largely concentrated along the axis of rotation in the leading term and that a rotating profile can be found in the second term. The leading term for Navier-Stokes flow will be an adequate Landau solution. The proofs rely upon a detailed analysis of the associated fundamental solution tensor.

MSC:
35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics
35B40 Asymptotic behavior of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76D07 Stokes and related (Oseen, etc.) flows
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