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arXiv · 2409.00537

On the uniqueness of the optimal control for 2-dimensional second grade fluids

Adilson Almeida·Nikolai V. Chemetov·Fernanda Cipriano
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Abstract

We study an optimal control problem with a quadratic cost functional for non-Newtonian fluids of differential type. More precisely, we consider the system governing the evolution of a second grade fluid filling a two-dimensional bounded domain, supplemented with a Navier slip boundary condition, and under certain assumptions on the size of the initial data and parameters of the model, we prove the second-order sufficient optimality conditions. Furthermore, we establish a global uniqueness result for the solutions of the first-order optimality system.

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Adilson Almeida, Nikolai V. Chemetov, Fernanda Cipriano. 2024-08-31. On the uniqueness of the optimal control for 2-dimensional second grade fluids. https://arxiv.org/abs/2409.00537

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