Geodesic
Stopping a viscous fluid by a feedback dissipative field: II. The stationary Navier-Stokes problem
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 257-270 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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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. 
@article{RLIN_2004_9_15_3-4_a8,
     author = {Antontsev, Stanislav Nikolaevich and D{\'\i}az, Jes\'us Ildefonso and de Oliveira, Hermenegildo Borges},
     title = {Stopping a viscous fluid by a feedback dissipative field: {II.} {The} stationary {Navier-Stokes} problem},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {257--270},
     year = {2004},
     volume = {Ser. 9, 15},
     number = {3-4},
     zbl = {1105.35074},
     mrnumber = {MR2148884},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_3-4_a8/}
}
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Antontsev, Stanislav Nikolaevich; Díaz, Jesús Ildefonso; de Oliveira, Hermenegildo Borges. Stopping a viscous fluid by a feedback dissipative field: II. The stationary Navier-Stokes problem. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 15 (2004) no. 3-4, pp. 257-270. http://geodesic.mathdoc.fr/item/RLIN_2004_9_15_3-4_a8/