Electronic Journal of Differential Equations, Vol. 2022 (2022), No. 22, pp. 1-12.

Title: Uniqueness for optimal control problems of two-dimensional second grade fluids
       
Authors: Adilson Almeida (Univ. Nova de Lisboa, Portugal)
         Nikolai V. Chemetov (Univ. of Sao Paulo,  Ribeirao Preto, SP, Brazil)
         Fernanda Cipriano (Univ. Nova de Lisboa, Portugal)

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.