A regularity criterion for a 3D chemo-repulsion system and its application to a bilinear optimal control problem

TL;DR

This paper establishes a regularity criterion for a 3D chemo-repulsion system, enabling the proof of global solutions and the derivation of optimality conditions for a related bilinear control problem.

Contribution

It introduces a new regularity criterion for 3D chemo-repulsion models and applies it to prove existence of global solutions and optimal controls.

Findings

Existence of weak solutions for the 3D chemo-repulsion system

A regularity criterion ensuring global strong solutions

Derivation of first-order optimality conditions for control

Abstract

In this paper we study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions and we establish a regularity criterion to get global in time strong solutions. As a consequence, we deduce the existence of a global optimal solution with bilinear control and, using a Lagrange multipliers theorem, we derive first-order optimality conditions for local optimal solutions.