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July  2008, 10(1): 1-18. doi: 10.3934/dcdsb.2008.10.1

Estimates of the wake for the 3D Oseen equations

Hyeong-Ohk Bae 1, and  Bum Ja Jin 2,

1. 

Ajou University, Suwon 443-749, South Korea
2. 

Mokpo National University, Mokpo, South Korea

Received  April 2007 Revised  November 2007 Published  April 2008

Since there is a wake for the Oseen flow, the convergence rates inside and outside the wake region might be different. The existence of the wake for the steady Oseen flow is given in Galdi [17]. 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.
Keywords: Oseen equations, exterior domain, spatial-temporal decay, wake..
Mathematics Subject Classification: Primary: 76D07; secondary: 35B40, 35Q3.
Citation: Hyeong-Ohk Bae, Bum Ja Jin. Estimates of the wake for the 3D Oseen equations. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 1-18. doi: 10.3934/dcdsb.2008.10.1
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