Remarks on Hierarchic Control for a Linearized Micropolar Fluids System in Moving Domains

TL;DR

This paper investigates a hierarchical control approach for linearized micropolar fluids in moving domains, establishing existence, uniqueness, and controllability results for a Stackelberg-Nash framework involving multiple players with different objectives.

Contribution

It introduces a novel Stackelberg control strategy for micropolar fluids in dynamic domains, proving existence, uniqueness, and controllability within this complex setting.

Findings

Existence and uniqueness of Nash equilibrium

Approximate controllability of the micropolar system

Solution characterization for the Stackelberg-Nash problem

Abstract

We study a Stackelberg strategy subject to the evolutionary linearized micropolar fluids equations in domains with moving boundaries, considering a Nash multi-objective equilibrium (non necessarily cooperative) for the "follower players" (as is called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following main results : the existence and uniqueness of Nash equilibrium and its characterization, the approximate controllability of the linearized micropolar system with respect to the leader control and the existence and uniqueness of the Stackelberg-Nash problem, where the optimality system for the leader is given.