On asymptotic stability of global solutions in the weak L2 space for the two-dimensional Navier–Stokes equations

Yasunori Maekawa

doi:10.1515/anly-2014-1302

Published by Oldenbourg Wissenschaftsverlag August 4, 2015

On asymptotic stability of global solutions in the weak L² space for the two-dimensional Navier–Stokes equations

Yasunori Maekawa

From the journal Analysis

https://doi.org/10.1515/anly-2014-1302

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Abstract

In this paper we prove the asymptotic stability of small global solutions in the weak L² space for the two-dimensional Navier–Stokes equations under a natural functional setting for the class of perturbations. Our result is a global one, that is, we do not impose any smallness on the perturbations.

Keywords: Navier–Stokes equations; large-time asymptotics; two-dimensional exterior domains; scale critical space; weak L2 space

MSC: 35B35; 35Q30; 76D05; 76D17

Funding source: Grant-in-Aid for Young Scientists (B)

Award Identifier / Grant number: 25800079

The author would like to thank Professor Hajime Koba for suggesting to use the space Lσ2(Ω)¯∥·∥L2,∞ as the class of perturbations in Theorem 1.1. The author is also grateful to the anonymous referee for his/her careful reading of the manuscript and useful comments.

Received: 2014-12-4

Revised: 2015-7-1

Accepted: 2015-7-14

Published Online: 2015-8-4

Published in Print: 2015-11-1

On asymptotic stability of global solutions in the weak L² space for the two-dimensional Navier–Stokes equations

Abstract

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