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Stopping a viscous fluid by a feedback dissipative field: II. The stationary Navier-Stokes problem

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Antontsev, Stanislav Nikolaevich and Díaz Díaz, Jesús Ildefonso and de Oliveira, Hermenegildo Borges (2004) Stopping a viscous fluid by a feedback dissipative field: II. The stationary Navier-Stokes problem. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, 15 (3-4). pp. 257-270. ISSN 1720-0768

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Abstract

We consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the Navier-Stokes system with a feed-back body forces field which depends on the velocity field. Since the presence of this type of non-linear terms is not standard in the fluid mechanics literature, we start by establishing some results about existence and uniqueness of weak solutions. Then, we prove how this fluid can be stopped at a finite distance of the semi-infinite strip entrance by means of this body forces field which depends in a sub-linear way on the velocity field. This localization effect is proved by reducing the problem to a fourth order non-linear one for which the localization of solutions is obtained by means of a suitable energy method.


Item Type:Article
Uncontrolled Keywords:Navier-Stokes system; Body forces field; Non-linear fourth order equation; Energy method; Localization effect
Subjects:Sciences > Physics
ID Code:30786
Deposited On:10 Jun 2015 10:38
Last Modified:12 Dec 2018 15:07

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