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arXiv · 2501.04548

Optimal Control of the Navier-Stokes equations via Pressure Boundary Conditions

Boris Vexler·Jakob Wagner
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Abstract

In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these boundary conditions not being well-posed for large times and/or data, we obtain wellposedness of the optimal control problem by choosing a proper tracking type term. In order to discuss the regularity of the optimal control, state and adjoint state, we present new results on $L^2(I;H^2(\Omega))$ regularity of solutions to a Stokes problem with mixed inhomogeneous boundary conditions.

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Boris Vexler, Jakob Wagner. 2025-01-08. Optimal Control of the Navier-Stokes equations via Pressure Boundary Conditions. https://doi.org/10.3934/mcrf.2025053

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