Communications on Pure and Applied Analysis (CPAA)

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

Pages: 1361 - 1393, Volume 13, Issue 4, July 2014      doi:10.3934/cpaa.2014.13.1361

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Peter Anthony - University of Surrey, Guildford, Gu27XH, Surrey, United Kingdom (email)
Sergey Zelik - Department of Mathematics, University of Surrey, Guildford, GU2 7XH, United Kingdom (email)

Abstract: The paper deals with the Navier-Stokes equations in a strip in the class of spatially non-decaying (in nite-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.

Keywords:  Navier-Stokes equations, unbounded domains, infinite-energy solutions.
Mathematics Subject Classification:  35B40, 35B45

Received: October 2013;      Revised: January 2014;      Available Online: February 2014.