# American Institute of Mathematical Sciences

2007, 2007(Special): 731-740. doi: 10.3934/proc.2007.2007.731

## Navier-Stokes problems modeled by evolution hemivariational inequalities

 1 Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow 2 Jagiellonian University, Faculty of Mathematics and Computer Sciences, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow, Poland

Received  September 2006 Revised  February 2007 Published  September 2007

In this paper we study an inequality problem for the evolution Navier-Stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain. The equations are nonlinear Navier-Stokes ones for the velocity and pressure with non-standard boundary conditions. We assume the nonslip boundary condition together with a Clarke subdifferential relation between the pressure and the normal components of the velocity. The existence of weak solutions to the model is proved by applying the regularized Galerkin method.
Citation: Stanislaw Migórski, Anna Ochal. Navier-Stokes problems modeled by evolution hemivariational inequalities. Conference Publications, 2007, 2007 (Special) : 731-740. doi: 10.3934/proc.2007.2007.731
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