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Infinite Energy Solutions for Navier-Stokes Equations in a Strip.

Anthony, Peter. (2013) Infinite Energy Solutions for Navier-Stokes Equations in a Strip. Doctoral thesis, University of Surrey (United Kingdom)..

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Abstract

This thesis deals with infinite energy solutions of the Navier-Stokes and Boussi-nesq equations in a strip. Here, the properly chosen Uniformly local Sobolev Spaces of functions are used as the phase spaces for the problem considered. The global well-posedness and dissipativity of the Navier-Stokes equations was first established in a paper by Zelik [37] on Spatially Nondecaying Solutions of the 2D Navier-Stokes equations in a strip. However, the proof given there contains error which emmanated from wrong estimation of the solutions of the auxiliary non-autonomous linear Stokes problem with non-homogeneous divergence. In this thesis, we correct the aforementioned error and show that the main results of [37], i. e the well-posedness of the Navier-Stokes problem in uniformly local spaces, remains true. Albeit, only a weaker version of the postulated results in [37] was amenable; therefore, we reworked most part of the non-linear theory as well as to show that they are sufficient for the well-posedness of the non-linear system. We also extended these results to the thermal convection problem in a strip and associated Boussinesq equations. We considered the temperature equation and proved, using maximum principle, the well-posedness of the full Boussinesq system in a Strip.

Item Type: Thesis (Doctoral)
Divisions : Theses
Authors : Anthony, Peter.
Date : 2013
Additional Information : Thesis (Ph.D.)--University of Surrey (United Kingdom), 2013.
Depositing User : EPrints Services
Date Deposited : 24 Apr 2020 15:26
Last Modified : 24 Apr 2020 15:26
URI: http://epubs.surrey.ac.uk/id/eprint/854881

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