Díaz Díaz, Jesús Ildefonso and Antontsev, S.N. and Oliveira, H.B. de (2004) Stopping a viscous fluid by a feedback dissipative external field: I. The stationary Stokes problem. Journal of Mathematical Fluid Mechanics, Volume (Number). p. 439. ISSN 14226928

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Official URL: http://www.springer.com/birkhauser/physics/journal/21
Abstract
In this work we consider a planar stationary flow of an incompressible viscous fluid in a semiinfinite strip governed by the standard Stokes system. We show how this fluid can be stopped at a finite distance of the entrance of the semiinfinite strip by means of a feedback source depending in a sublinear way on the velocity field. This localization effect is proved reducing the problem to a nonlinear biharmonic type one for which the localization of solutions is obtained by means of the application of an energy method, in the spirit of the monograph by Antontsev, Díaz and Shmarev [5]. Since the presence of the nonlinear terms defined by the source is not standard in the fluid mechanics literature, we establish also some results about the existence and uniqueness of weak solutions for this problem.
Item Type:  Article 

Uncontrolled Keywords:  Stokes system, Feedback dissipative field, Non linear higher order equation, Energy method, Localization effect. 
Subjects:  Sciences > Mathematics > Differential equations 
ID Code:  12342 
Deposited On:  07 Mar 2011 15:57 
Last Modified:  06 Feb 2014 09:22 
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