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Infinite Energy Solutions for Damped Navier-Stokes Equations in R2

Zelik, S (2012) Infinite Energy Solutions for Damped Navier-Stokes Equations in R2 Journal of Mathematical Fluid Mechanics.

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Abstract

We study the so-called damped Navier-Stokes equations in the whole 2D space. The global well-posedness, dissipativity and further regularity of weak solutions of this problem in the uniformly-local spaces are verified based on the further development of the weighted energy theory for the Navier-Stokes type problems. Note that any divergent free vector field $u_0\in L^\infty(\mathbb R^2)$ is allowed and no assumptions on the spatial decay of solutions as $|x|\to\infty$ are posed. In addition, applying the developed theory to the case of the classical Navier-Stokes problem in R2, we show that the properly defined weak solution can grow at most polynomially (as a quintic polynomial) as time goes to infinity.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
AuthorsEmailORCID
Zelik, SUNSPECIFIEDUNSPECIFIED
Date : 26 March 2012
Identification Number : 10.1007/s00021-013-0144-3
Related URLs :
Additional Information : This is an arXiv version of the paper.
Depositing User : Symplectic Elements
Date Deposited : 07 Jan 2015 18:25
Last Modified : 08 Jan 2015 02:33
URI: http://epubs.surrey.ac.uk/id/eprint/806843

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