Analysis of Robin-boundary control for the Boussinesq equations
Abstract
In this paper, we study an optimal boundary control problem for the Boussinesq equations, which couple the time-dependent Navier-Stokes system with a heat equation, where the control enters through a Robin boundary condition on temperature. We begin by establishing the well-posedness of the optimization problem via a variational framework. We then derive both first- and second-order optimality conditions, including explicit characterizations of the adjoint state and the optimal control. Next, we perform a detailed numerical analysis of a fully discrete scheme: using finite elements in space and a semi-implicit scheme in time, combined with variational discretization for the control. We present rigorous a prior error estimates for the state, adjoint state, and control variables. Numerical experiments are provided to validate our theoretical results.
Keywords
Cite
@article{arxiv.2603.01600,
title = {Analysis of Robin-boundary control for the Boussinesq equations},
author = {Wei Gong and Dongdong Liang and Xianbing Luo and Changlun Ye},
journal= {arXiv preprint arXiv:2603.01600},
year = {2026}
}