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September  2006, 5(3): 583-596. doi: 10.3934/cpaa.2006.5.583

On a variational inequality for the Navier-Stokes operator with variable viscosity

G. M. de Araújo 1, and  S. B. de Menezes 1,

1. 

Universidade Federal do Pará, Departamento de Matematica-CCEN, 66.075-110 Belém Pará, Brazil, Brazil

Received  June 2005 Revised  February 2006 Published  June 2006

In this paper we investigate the unilateral problem for the operator $L$ perturbed of Navier-Stokes operator in a cylindrical case, where

$Lu=u'-(\nu_0+\nu_1||u(t)||^2)\Delta u+(u.\nabla )u-f+\nabla p.$

The mixed problem for the operator $L$ was proposed by J. L. Lions [6]. Using an appropriate penalization, we obtain a variational inequality for the Navier-Stokes perturbed system.

Keywords: variational inequality., Navier-Stokes equations, variable viscosity.
Mathematics Subject Classification: Primary: 35K60, 35Q30; Secondary: 35F3.
Citation: G. M. de Araújo, S. B. de Menezes. On a variational inequality for the Navier-Stokes operator with variable viscosity. Communications on Pure and Applied Analysis, 2006, 5 (3) : 583-596. doi: 10.3934/cpaa.2006.5.583
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