On bounds of the drag for Stokes flow around a body without thickness

Didier Bresch

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 4, page 665-679
  • ISSN: 0010-2628

Abstract

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This paper is devoted to lower and upper bounds of the hydrodynamical drag T for a body in a Stokes flow. We obtain the upper bound since the solution for a flow in an annulus and therefore the hydrodynamical drag can be explicitly derived. The lower bound is obtained by comparison to the Newtonian capacity of a set and with the help of a result due to J. Simon [ 10 ] . The chosen approach provides an interesting lower bound which is independent of the interior of the body.

How to cite

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Bresch, Didier. "On bounds of the drag for Stokes flow around a body without thickness." Commentationes Mathematicae Universitatis Carolinae 38.4 (1997): 665-679. <http://eudml.org/doc/248089>.

@article{Bresch1997,
abstract = {This paper is devoted to lower and upper bounds of the hydrodynamical drag $T$ for a body in a Stokes flow. We obtain the upper bound since the solution for a flow in an annulus and therefore the hydrodynamical drag can be explicitly derived. The lower bound is obtained by comparison to the Newtonian capacity of a set and with the help of a result due to J. Simon $\,[10]$. The chosen approach provides an interesting lower bound which is independent of the interior of the body.},
author = {Bresch, Didier},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Stokes flows; hydrodynamical drag; lower and upper bounds; lower and upper bounds},
language = {eng},
number = {4},
pages = {665-679},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On bounds of the drag for Stokes flow around a body without thickness},
url = {http://eudml.org/doc/248089},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Bresch, Didier
TI - On bounds of the drag for Stokes flow around a body without thickness
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 4
SP - 665
EP - 679
AB - This paper is devoted to lower and upper bounds of the hydrodynamical drag $T$ for a body in a Stokes flow. We obtain the upper bound since the solution for a flow in an annulus and therefore the hydrodynamical drag can be explicitly derived. The lower bound is obtained by comparison to the Newtonian capacity of a set and with the help of a result due to J. Simon $\,[10]$. The chosen approach provides an interesting lower bound which is independent of the interior of the body.
LA - eng
KW - Stokes flows; hydrodynamical drag; lower and upper bounds; lower and upper bounds
UR - http://eudml.org/doc/248089
ER -

References

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  1. Allaire G., Homogénéisation des équations de Stokes et de Navier-Stokes, Thesis, Pierre et Marie Curie University, France, 1989. 
  2. Bello J.A., Fernandez-Cara E., Lemoine J., Simon J., The differentiability of the drag with respect to the variations of a lipschitz domain in Navier-Stokes flow, SIAM J. Control Optim. 35 2 (1997), 626-640. (1997) MR1436642
  3. Cioranescu D., Murat F., Un terme étrange venu d'ailleurs, Non linear partial differential equations and their applications, Collège de France Seminar, 2 et 3 ed. by H. Brezis and J.L. Lions, Research Notes in Mathematics 60 et 70, Pitman, London, 1982. Zbl0498.35034
  4. Dautray R., Lions J.L., Analyse mathématique et calcul numérique pour les Sciences et les Techniques (Chapitre II L'opérateur de Laplace), INSTN C.E.A., 1985. 
  5. Gilbart D., Trudinger N.S., Elliptic partial differential equation of second order, second edition, Springer Verlag, 1983. MR0737190
  6. Godbillon C., Eléments de Topologie Algébrique, Hermann Paris, Collection méthodes, 1971. Zbl0907.55001MR0301725
  7. Heywood J.G., On some paradoxes concerning two dimensional Stokes flow past an obstacle, Indiana University Mathematics Journal 24 5 (1974), 443-450. (1974) Zbl0315.35075MR0410123
  8. Mossino J., Inégalités Isopérimètriques et applications en physique, Travaux en cours, Hermann, éditeurs des Sciences et des Arts, Paris, 1992. Zbl0537.35002MR0733257
  9. Sanchez-Hubert J., Sanchez-Palencia E., Introduction aux méthodes asymptotiques et à l'homogénéisation, Masson, 1992. 
  10. Simon J., On a result due to L.A. Caffarelli and A. Friedman concerning the asymptotic behavior of a plasma, Non linear partial differential equations and their applications, Collège de France, Seminar volume IV, Research Notes in Mathematics, Pitman, London, 1983, pp.214-239. Zbl0555.35045MR0716520
  11. Simon J., Distributions à valeurs vectorielles, to appear. 
  12. Stokes G.G., On the effect of the internal friction of fluids on the motion of pendulums., Trans. Camb. Phil. Soc. 9 Part III (1851), 8-106. (1851) 

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