A Quasi-Variational-Hemivariational Inequality for Incompressible Navier-Stokes System with Bingham Fluid
Stanisław Migórski, Sylwia Dudek
Abstract
Abstract In this paper we examine a class of elliptic quasi-variational inequalities, which involve a constraint set and a set-valued map. First, we establish the existence of a solution and the compactness of the solution set. The approach is based on results for an elliptic variational inequality and the Kakutani-Ky Fan fixed point theorem. Next, we prove an existence and compactness result for a quasi-variational-hemivariational inequality. The latter involves a locally Lipschitz continuous functional and a convex potential. Finally, we present an application to the stationary incompressible Navier-Stokes equation with mixed boundary conditions which model a generalized Newtonian fluid of Bingham type.
Topics & Concepts
MathematicsCompact spaceLipschitz continuityMathematical analysisCompressibilityWeak solutionVariational inequalityBoundary (topology)Type (biology)Regular polygonConstraint (computer-aided design)Applied mathematicsPhysicsGeometryBiologyThermodynamicsEcologyContact Mechanics and Variational InequalitiesElasticity and Material ModelingNumerical methods in engineering