Comptes Rendus
no. 17-18
Ordinary Differential Equations
Anti symmetric solutions of non-linear laminar flow between parallel permeable disks
[Solution antisymétrique d'un écoulement laminaire non linéaires entre deux disques parallèles perméables]

Présenté par : Haïm Brezis

Adimurthi1 ; A. Karthik2
1 Department of Mathematics, TIFR Center, Bangalore 560012, India
2 Bangalore, India
Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 935-938.

On étudie des écoulements similaires entre deux disques parallèles infinis, perméables, dans le cas où les taux d'aspiration ou d'injection sont égaux ; on déduit les équations de mouvement en utilisant la fonction de courant. La méthode de plan mobile permet de démontrer l'antisymétrie des solutions d'un problème aux limites pour une équation différentielle d'ordre quatre. L'antisymétrie mise en évidence est conforme aux résultats numériques connus.

The equations describing similarity solutions for flow between infinite parallel permeable disks with equal rates of suction or injection at the walls is derived using the stream function. This leads to a fourth order non-linear Ordinary Differential Equation. This equation is shown to admit anti-symmetric solutions using the moving plane method.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.05.018
Adimurthi 1 ; A. Karthik 2

1 Department of Mathematics, TIFR Center, Bangalore 560012, India
2 Bangalore, India 
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Adimurthi; A. Karthik. Anti symmetric solutions of non-linear laminar flow between parallel permeable disks. Comptes Rendus. Mathématique, Volume 346 (2008) no. 17-18, pp. 935-938. doi : 10.1016/j.crma.2008.05.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.05.018/

[1] A.S. Berman Laminar flow in channels with porous walls, J. Appl. Phys., Volume 24 (1953), pp. 1232-1235

[2] P.A. Dinesh, A. Karthik, Study of nonlinear laminar flow between parallel permeable disks, 2006, preprint

[3] B. Gidas; W.M. Ni; L. Nirenberg Symmetry of positive solutions of non-linear elliptic equations in Rn, Math. Anal. Appl. Part A, Volume 7 (1981), pp. 369-402

[4] W.A. Robinson The Existence of multiple solutions for the laminar flow in uniformly porous channel with suction at both walls, J. Engrg. Math., Volume 10 (1976), pp. 23-40

[5] J.R. Sellars Laminar flow in channels with porous walls at high suction Reynolds number, J. Appl. Phys., Volume 26 (1955), pp. 489-490

[6] F.M. Skalak; C.Y. Wang On the non-unique solutions of laminar flow through a porous tube or channel, SIAM J. Appl. Math., Volume 34 (1978), pp. 535-544

[7] S.W. Yuan Further investigations of laminar flow in channels with porous walls, J. Appl. Phys., Volume 27 (1956), pp. 267-269

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