## Journal of the Mathematical Society of Japan

### On stability of Leray's stationary solutions of the Navier–Stokes system in exterior domains

Hajime KOBA

#### Abstract

This paper studies the stability of a stationary solution of the Navier–Stokes system in $3$-D exterior domains. The stationary solution is called a Leray's stationary solution if the Dirichlet integral is finite. We apply an energy inequality and maximal $L^p$-in-time regularity for Hilbert space-valued functions to derive the decay rate with respect to time of energy solutions to a perturbed Navier–Stokes system governing a Leray's stationary solution.

#### Article information

Source
J. Math. Soc. Japan, Volume 69, Number 1 (2017), 373-396.

Dates
First available in Project Euclid: 18 January 2017

https://projecteuclid.org/euclid.jmsj/1484730029

Digital Object Identifier
doi:10.2969/jmsj/06910373

Mathematical Reviews number (MathSciNet)
MR3597558

Zentralblatt MATH identifier
1368.35208

Subjects
Primary: 93D20: Asymptotic stability

#### Citation

KOBA, Hajime. On stability of Leray's stationary solutions of the Navier–Stokes system in exterior domains. J. Math. Soc. Japan 69 (2017), no. 1, 373--396. doi:10.2969/jmsj/06910373. https://projecteuclid.org/euclid.jmsj/1484730029

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