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Navier-Stokes problems modeled by evolution hemivariational inequalities

Pages: 731 - 740, Issue Special, September 2007

 Abstract        Full Text (217.0K)              

Stanislaw Migórski - Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow, Poland (email)
Anna Ochal - Jagiellonian University, Faculty of Mathematics and Computer Sciences, Institute of Computer Science, ul. Nawojki 11, 30-072 Krakow, Poland (email)

Abstract: 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:  Hemivariational inequality, Navier-Stokes equation, nonconvex, subdifferential, Galerkin method, inclusion.
Mathematics Subject Classification:  Primary: 76D05, 47J20, 35K85, 74G25, 35Q30; Secondary: 35R70, 49J40.

Received: September 2006;      Revised: February 2007;      Published: September 2007.