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

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  • 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.

    Mathematics Subject Classification: Primary: 35K60, 35Q30; Secondary: 35F30.


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