# On the rate of decay of the oseen semigroup in exterior domains and its application to Navier-Stokes equation

Yuko Enomoto, Yoshihiro Shibata

Research output: Contribution to journalArticle

32 Citations (Scopus)

### 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.

Original language English 339-367 29 Journal of Mathematical Fluid Mechanics 7 3 https://doi.org/10.1007/s00021-004-0132-8 Published - 2005 Aug

### Fingerprint

Stokes flow
Exterior Domain
Navier-Stokes equations
Flow velocity
Navier-Stokes equation
flow velocity
infinity
Navier Stokes equations
Navier-Stokes Equations
Semigroup
Decay
Convergence of Solutions
Optimal Rate of Convergence
Stokes Flow
Stability Theory
decay
estimates
Navier-Stokes
n-dimensional
Infinity

### Keywords

• Exterior domain
• L -L estimate
• Oseen semigroup
• Stability
• Stationary solution

### ASJC Scopus subject areas

• Materials Science (miscellaneous)
• Oceanography
• Fluid Flow and Transfer Processes
• Applied Mathematics

### Cite this

In: Journal of Mathematical Fluid Mechanics, Vol. 7, No. 3, 08.2005, p. 339-367.

Research output: Contribution to journalArticle

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