Optimal control problem related to the non-stationary Boussinesq system with Navier-slip boundary conditions
Abstract
In this paper, we analyze a distributed optimal control problem associated to the strong solutions of a 3D Boussinesq system with Navier-slip boundary conditions. Since the existence of strong (global) solutions is an open question, we consider a suitable cost functional such that any weak solution, satisfying a regularity criterion, is also a global-in-time strong solution. Then, we prove the existence of optimal solutions and deduce the differentiability of the map control-to-state via the implicit function theorem. As a consequence, we obtain first-order necessary optimality conditions for local optimal solutions.
Fields of Study & Subjects
Stability and Controllability of Differential Equations
Navier-Stokes equation solutions
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Mathematical Control and Related Fields
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 0
- Issue
- 0
- Publication date
- 1 January 2026