Calmness of the solution mapping of Navier-Stokes problems modeled by hemivariational inequalities

Abstract

The main purpose of this paper is to find conditions for Hölder calmness of the solution mapping, viewed as a function of the boundary data, of a hemivariational inequality governed by the Navier-Stokes operator. To this end, a more abstract model is studied first: a class of parametric equilibrium problems defined by trifunctions. The presence of trifunctions allows the extension of the monotonicity notions and of the duality principle in the theory of equilibrium problems.