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Journal of Mathematical Fluid Mechanics

, Volume 7, Issue 3, pp 339–367 | Cite as

On the Rate of Decay of the Oseen Semigroup in Exterior Domains and its Application to Navier–Stokes Equation

  • Yuko EnomotoEmail author
  • Yoshihiro Shibata
Original Paper

Abstract.

We prove L p -L q estimates of the Oseen semigroup in n-dimensional exterior domains \((n\,\geqslant\, 3),\) which refine and improve those obtained by Kobayashi and Shibata [15]. As an application, we give a globally in time stability theory for the stationary Navier–Stokes flow whose velocity at infinity is a non-zero constant vector. We thus extend the result of Shibata [21]. In particular, we find an optimal rate of convergence of solutions of the non-stationary problem to those of the corresponding stationary problem.

Mathematics Subject Classification (2000).

35B40 35M20 73B30 

Keywords.

Oseen semigroup LpLq estimate exterior domain stability stationary solution 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of Mathematical Sciences, School of Science and EngineeringWaseda UniversityTokyoJapan

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