Electron. J. Differential Equations, Vol. 2022 (2022), No. 22, pp. 1-12.
Uniqueness for optimal control problems of two-dimensional second grade fluids
Adilson Almeida, Nikolai V. Chemetov, Fernanda Cipriano
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.
Under certain assumptions on the size of the initial data and parameters of the model,
we prove second-order sufficient optimality conditions.
Furthermore, we establish a global uniqueness result for the solutions of the first-order
optimality system.
Submitted September 6, 2021. Published March 18, 2022.
Math Subject Classifications: 35R60, 49K20, 60G15, 60H15, 76D55.
Key Words: Second grade fluids; optimal control; uniqueness.
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Adilson Almeida
Centro de Matemática e Aplicações (CMA)
Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa,
Portugal
email: ama.almeida@campus.fct.unl.pt
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Nikolai V. Chemetov
Department of Computing and Mathematics
University of São Paulo
14040-901 Ribeirão Preto - SP, Brazil
email: nvchemetov@gmail.com
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Fernanda Cipriano
Centro de Matemática e Aplica\c cões (CMA) FCT/UNL and
Departamento de Matemática
Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa,
Portugal
email: cipriano@fct.unl.pt
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