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

Navier-Stokes problems modeled by evolution hemivariational inequalities

Stanislaw Migórski 1, and  Anna Ochal 2,

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.
Keywords: Galerkin method, nonconvex, inclusion., Hemivariational inequality, subdifferential, Navier-Stokes equation.
Mathematics Subject Classification: Primary: 76D05, 47J20, 35K85, 74G25, 35Q30; Secondary: 35R70, 49J4.
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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