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

TL;DR

This paper investigates conditions under which the solution mapping of Navier-Stokes problems modeled by hemivariational inequalities exhibits Holder calmness, extending equilibrium problem theory with trifunctions.

Contribution

It introduces a framework for analyzing Holder calmness of solution mappings in Navier-Stokes hemivariational inequalities using a generalized equilibrium problem model with trifunctions.

Findings

Established conditions for Holder calmness of solution mappings.

Extended monotonicity notions to trifunction-based equilibrium problems.

Provided a theoretical foundation for stability analysis of Navier-Stokes hemivariational inequalities.

Abstract

The main purpose of this paper is to find conditions for Holder 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.