Infinite-energy solutions for the Navier-Stokes equations in a strip revisited

Peter Anthony; Sergey Zelik

doi:10.3934/cpaa.2014.13.1361

Article Contents

2014, Volume 13, Issue 4: 1361-1393. Doi: 10.3934/cpaa.2014.13.1361

This issue Previous Article Next Article Global existence of solutions for the thermoelastic Bresse system

Infinite-energy solutions for the Navier-Stokes equations in a strip revisited

Peter Anthony^1, and
Sergey Zelik^2,

1.
University of Surrey, Guildford, Gu27XH, Surrey
2.
Department of Mathematics, University of Surrey, Guildford, GU2 7XH

Received: September 30, 2013

Revised: December 31, 2013

Published: June 2015

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Abstract

The paper deals with the Navier-Stokes equations in a strip in the class of spatially non-decaying (innite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier-Stokes equations in a strip in such spaces has been rst established in [22]. However, the proof given there contains a rather essential error and the aim of the present paper is to correct this error and to show that the main results of [22] remain true.

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Mathematics Subject Classification: 35B40, 35B45.

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