A function space approach to the shape optimization of the Boussinesq system
Abstract
We investigate a shape optimization problem for a heat-conducting fluid governed by a Boussinesq system. The main goal is to determine an optimal domain shape that yields a temperature distribution as uniform as possible. Initially, we analyze the state problem, prove its well-posedness and establish a local boundary regularity result for the weak solution. We then demonstrate the existence of an optimal shape and derive a first-order optimality condition. This requires the derivation and analysis of the adjoint system associated with the Boussinesq model, as well as a rigorous treatment of the directional derivatives of the objective functional under appropriate domain perturbations. Finally, we present numerical experiments that illustrate and support the theoretical findings.
Cite
@article{arxiv.2504.15522,
title = {A function space approach to the shape optimization of the Boussinesq system},
author = {Andrea Ceretani and Weiwei Hu and Lin Mu and Carlos Rautenberg},
journal= {arXiv preprint arXiv:2504.15522},
year = {2025}
}