On the confinement of a viscous fluid by means of a feedback external field |
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Authors: | S N Antontsev J I Díaz H B de
Oliveira |
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Institution: | a Departamento de Matemática, Universidade da Beira Interior, 6201-001, Covilhã, Portugal;b Facultad de Matematicas, Universidad Complutense, 28040, Madrid, Spain;c Faculdade de Ciências e Tecnologia, Universidade do Algarve, 8000-062, Faro, Portugal |
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Abstract: | In this work we consider a planar stationary flow of an incompressible viscous fluid in a semi-infinite strip governed by the standard Stokes system. We show how this fluid can be stopped at a finite distance from the entrance of the semi-infinite strip by means of a feedback source depending in a sublinear way on the velocity field. This localization effect is proved by reducing the problem to a non-linear biharmonic type one for which the localization of solutions is obtained through the application of an energy method, in the spirit of the monograph by S.N. Antontsev, J.I. Díaz and S.I. Shmarev (Energy Methods for Free Boundary Problems: Applications to Non-Linear PDEs and Fluid Mechanics, Birkäuser, Boston, 2002). Since the presence of the non-linear terms defined by the source is not standard in fluid mechanics literature, we give also some results about the existence and uniqueness of weak solutions for this problem. To cite this article: S.N. Antontsev et al., C. R. Mecanique 330 (2002) 797–802. |
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Keywords: | computational fluid mechanics Stokes system feedback dissipative field non-linear higher order equation energy method localization effectAuthor Keywords: mé canique des fluides numé rique systé me de Stokes champ avec mé moire dissipatif equations non-linè aires d'ordres superieures mé thode d'é nergie effet de localisation |
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