| Title:
|
On bounds of the drag for Stokes flow around a body without thickness (English) |
| Author:
|
Bresch, Didier |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
665-679 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Stokes flows |
| Keyword:
|
hydrodynamical drag |
| Keyword:
|
lower and upper bounds |
| MSC:
|
35Q35 |
| MSC:
|
76D07 |
| idZBL:
|
Zbl 1042.76516 |
| idMR:
|
MR1603690 |
| . |
| Date available:
|
2009-01-08T18:37:12Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118965 |
| . |
| Reference:
|
[1] Allaire G.: Homogénéisation des équations de Stokes et de Navier-Stokes.Thesis, Pierre et Marie Curie University, France, 1989. |
| Reference:
|
[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. MR 1436642 |
| Reference:
|
[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. Zbl 0498.35034 |
| Reference:
|
[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. |
| Reference:
|
[5] Gilbart D., Trudinger N.S.: Elliptic partial differential equation of second order.second edition, Springer Verlag, 1983. MR 0737190 |
| Reference:
|
[6] Godbillon C.: Eléments de Topologie Algébrique.Hermann Paris, Collection méthodes, 1971. Zbl 0907.55001, MR 0301725 |
| Reference:
|
[7] Heywood J.G.: On some paradoxes concerning two dimensional Stokes flow past an obstacle.Indiana University Mathematics Journal 24 5 (1974), 443-450. Zbl 0315.35075, MR 0410123 |
| Reference:
|
[8] Mossino J.: Inégalités Isopérimètriques et applications en physique.Travaux en cours, Hermann, éditeurs des Sciences et des Arts, Paris, 1992. Zbl 0537.35002, MR 0733257 |
| Reference:
|
[9] Sanchez-Hubert J., Sanchez-Palencia E.: Introduction aux méthodes asymptotiques et à l'homogénéisation.Masson, 1992. |
| Reference:
|
[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. Zbl 0555.35045, MR 0716520 |
| Reference:
|
[11] Simon J.: Distributions à valeurs vectorielles.to appear. |
| Reference:
|
[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. |
| . |
