Electron. J. Diff. Equ., Vol. 2012 (2012), No. 37, pp. 1-10.

A non-resonance problem for non-Newtonian fluids

Omar Chakrone, Okacha Diyer, Driss Sbibih

Abstract:
In this article we study a highly nonlinear problem which describes a non-Newtonian fluid in a specific domain (symmetric channel). This fluid is subjected to pressure of known differences between two parallel plates. We establish the existence and uniqueness of a weak solution. Our solution method is based on a minimization technique when the nonlinearity is asymptotically on the left of the first eigenvalue of the operator k-Laplacian.

Submitted May 17, 2011. Published March 7, 2012.
Math Subject Classifications: 74S05, 76T10.
Key Words: Non-Newtonian fluid; k-Laplacian operator; eigenvalues; variational method.

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Omar Chakrone
Université Mohammed I
Faculté des sciences
Laboratoire LANOL, Oujda, Maroc
email: chakrone@yahoo.fr
Okacha Diyer
Université Mohammed I
Ecole Supérieure de Technologie
Laboratoire MATSI, Oujda, Maroc
email: odiyer@yahoo.fr
Driss Sbibih
Université Mohammed I
Ecole Supérieure de Technologie
Laboratoire MATSI, Oujda, Maroc
email: sbibih@yahoo.fr

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