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Boundary layers for Oseen’s type equation in space dimension three. (English) Zbl 0912.35125
Summary: We treat linearized Navier-Stokes equations of Oseen’s type with large Reynolds number and study the corresponding boundary layers. We consider the flow in a channel in three-dimensional space, extending the results previously established in [the authors, Indiana Univ. Math. J. 45, 863-916 (1996; Zbl 0881.35097)] for two-dimensional space. The results here are stronger than those in (loc. cit.): We prove results on the strong convergence in $$H^1$$ and $$L^\infty$$ (uniform) norms and provide a corrector which is divergence-free and matches the boundary value of the inviscid solution.

##### MSC:
 35Q30 Navier-Stokes equations 76D10 Boundary-layer theory, separation and reattachment, higher-order effects 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics