On the existence of optimal and ϵ−optimal feedback controls for stochastic second grade fluids

Cipriano, Fernanda; Pereira, Diogo

doi:10.1016/j.jmaa.2019.03.064

Cited by 9 publications

(5 citation statements)

References 10 publications

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“…A semi-analytical approach for the investigation of rivulet flows of non-Newtonian fluids was developed in [28,29]. Finally, we mention mathematical studies devoted to the existence and uniqueness of solutions to PDEs describing second grade fluid flows [30][31][32][33][34][35][36] as well as to optimal flow control and controllability problems [37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions

Baranovskii

2024

Polymers

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This paper deals with an initial-boundary value problem modeling the unidirectional pressure-driven flow of a second grade fluid in a plane channel with impermeable solid walls. On the channel walls, Navier-type slip boundary conditions are stated. Our aim is to investigate the well-posedness of this problem and obtain its analytical solution under weak regularity requirements on a function describing the velocity distribution at initial time. In order to overcome difficulties related to finding classical solutions, we propose the concept of a generalized solution that is defined as the limit of a uniformly convergent sequence of classical solutions with vanishing perturbations in the initial data. We prove the unique solvability of the problem under consideration in the class of generalized solutions. The main ingredients of our proof are a generalized Abel criterion for uniform convergence of function series and the use of an orthonormal basis consisting of eigenfunctions of the related Sturm–Liouville problem. As a result, explicit expressions for the flow velocity and the pressure in the channel are established. The constructed analytical solutions favor a better understanding of the qualitative features of time-dependent flows of polymer fluids and can be applied to the verification of relevant numerical, asymptotic, and approximate analytical methods.

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Section: Introductionmentioning

confidence: 99%

Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions

Baranovskii

2024

Polymers

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“…To the best of our knowledge, the control problem for the second grade fluids (differential type) has been addressed for the first time in [3], where the authors proved the existence of a 2D-deterministic optimal control and deduced the first order optimality conditions. Later on, the control problem for 2Dstochastic second grade fluid models have been studied in [9,12]. Recently in [27], the authors tackled the control problem for 2D-deterministic third grade fluids.…”

Section: Introductionmentioning

confidence: 99%

Optimal control of two dimensional third grade fluids

Yassine¹,

Cipriano

2023

Journal of Mathematical Analysis and Applications

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“…In the deterministic context, the optimal control problem for the second grade fluid equations was studied in the articles [2,3], while the optimal control of the stochastic dynamic has been addressed in [13,18]. The authors established the existence of an optimal solution for the control problem, and by analyzing the linearized state equation as well as the adjoint equation deduced the first-order optimality conditions.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness for optimal control problems of two-dimensional second grade fluids

Almeida¹,

Chemetov²,

Cipriano³

2022

ejde

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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.

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On the existence of optimal and ϵ−optimal feedback controls for stochastic second grade fluids

Cited by 9 publications

References 10 publications

Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions

Analytical Solutions to the Unsteady Poiseuille Flow of a Second Grade Fluid with Slip Boundary Conditions

Optimal control of two dimensional third grade fluids

Uniqueness for optimal control problems of two-dimensional second grade fluids

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