Hemivariational Inequalities for Stationary Navier-Stokes Equations


S. Migórski, migorski(at)softlab.ii.uj.edu.pl
A. Ochal, ochal(at)softlab.ii.uj.edu.pl
       Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland

Pages: 22

Abstract: In this paper we study a class of inequality problems for the stationary 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 and uniqueness of weak solutions to the model are proved by using a surjectivity result for pseudomonotone maps. We also establish a result on the dependence of the solution set with respect to a locally Lipschitz superpotential appearing in the boundary condition. 

Keywords: Navier-Stokes equation, hemivariational inequality, subdifferential, pseudomonotone, nonconvex. 

Published: Journal of Mathematical Analysis and Applications, 306 (2005), 197-217.