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Estimates of the wake for the 3D Oseen equations. (English) Zbl 1141.76021
Summary: Since there is a wake for Oseen flow, the convergence rates inside and outside the wake region might be different. The existence of the wake for steady Oseen flow is given in G. P. Galdi [An introduction to the mathematical theory of the Navier-Stokes equations. Vol. 1: Linearized steady problems. Springer Tracts in Natural Philosophy 38. New York, NY: Springer Verlag. xi (1994; Zbl 0949.35004)]. We estimate these rates for the non-steady case. In order to do that, we estimate the \(L^p\) spatial-temporal decay rates of solutions of incompressible Oseen flow in an exterior domain. For the spatial-temporal decays, we consider weights of the form \(|x|\) and \(|x-{\mathbf u}_\infty t|\), where \(x\) is the spatial variable and \({\mathbf u}_\infty\) is the constant velocity at infinity. From our estimates, we conclude the convergence inside the wake region might be slower than outside the wake region.

MSC:
76D07 Stokes and related (Oseen, etc.) flows
35Q35 PDEs in connection with fluid mechanics
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