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Stability for the 3D Navier–Stokes Equations with Nonzero far Field Velocity on Exterior Domains

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Abstract

Concerning to the non-stationary Navier–Stokes flow with a nonzero constant velocity at infinity, just a few results have been obtained, while most of the results are for the flow with the zero velocity at infinity. The temporal stability of stationary solutions for the Navier–Stokes flow with a nonzero constant velocity at infinity has been studied by Enomoto and Shibata (J Math Fluid Mech 7:339–367, 2005), in L p spaces for p ≥ 3. In this article, we first extend their result to the case \({\frac{3}{2} < p}\) by modifying the method in Bae and Jin (J Math Fluid Mech 10:423–433, 2008) that was used to obtain weighted estimates for the Navier–Stokes flow with the zero velocity at infinity. Then, by using our generalized temporal estimates we obtain the weighted stability of stationary solutions for the Navier–Stokes flow with a nonzero velocity at infinity.

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Authors and Affiliations

  1. Department of Financial Engineering, Ajou University, Suwon, 443-749, Republic of Korea

    Hyeong-Ohk Bae

  2. Department of Mathematics, Hallym University, Chuncheon, 200-702, Republic of Korea

    Jaiok Roh

Authors
  1. Hyeong-Ohk Bae
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  2. Jaiok Roh
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Correspondence to Hyeong-Ohk Bae.

Additional information

Communicated by D. Chae

This work was supported by Korea Research Foundation Grant funded by the Korean Government (the first author by MOERD, Basic Research Promotion Fund, KRF-2007-314-C00020 and the second author by KRF-2008-531-C00008).

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Bae, HO., Roh, J. Stability for the 3D Navier–Stokes Equations with Nonzero far Field Velocity on Exterior Domains. J. Math. Fluid Mech. 14, 117–139 (2012). https://doi.org/10.1007/s00021-010-0040-z

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