The Time Optimal Control of Two Dimensional Convective Brinkman–Forchheimer Equations

Mohan, Manil T.

doi:10.1007/s00245-021-09748-w

Cited by 4 publications

(6 citation statements)

References 37 publications

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“…In fact, one can show that u ∈ C([0, T ]; H) satisfying the energy equality (17) for r = 3, since Theorem 4.1, [20] (see Lemma 2.5, [20] for proper approximations) is applicable as u ∈ L 4 (0, T ; L 4 ), for r = 3. Moreover, the existence of a strong solution (Theorem 2.10, [31]) to the system ( 15) also ensures that u ∈ C([0, T ]; H).…”

Section: Bilinear Operator Let Us Now Define the Trilinear Formmentioning

confidence: 99%

“…Various optimal control problems governed by Navier-Stokes equations have been considered in [4,15,41,42], etc and the references therein. Pontryagin's maximum principle for the time optimal control of 2D CBF equations is established in [31]. In this work, we consider the optimal control problems like total energy minimization, minimization of enstrophy, etc, governed by the two dimensional CBF equations (1).…”

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confidence: 99%

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Optimal control problems governed by two dimensional convective Brinkman-Forchheimer equations

Mohan¹

2022

EECT

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The convective Brinkman-Forchheimer (CBF) equations describe the motion of incompressible viscous fluids through a rigid, homogeneous, isotropic, porous medium and is given byIn this work, we consider some distributed optimal control problems like total energy minimization, minimization of enstrophy, etc governed by the two dimensional CBF equations with the absorption exponent r = 1, 2 and 3. We show the existence of an optimal solution and the first order necessary conditions of optimality for such optimal control problems in terms of the Euler-Lagrange system. Furthermore, for the case r = 3, we show the second order necessary and sufficient conditions of optimality. We also investigate an another control problem which is similar to that of the data assimilation problems in meteorology of obtaining unknown initial data, when the system under consideration is 2D CBF equations, using optimal control techniques.

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Section: Bilinear Operator Let Us Now Define the Trilinear Formmentioning

confidence: 99%

mentioning

confidence: 99%

Optimal control problems governed by two dimensional convective Brinkman-Forchheimer equations

Mohan¹

2022

EECT

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“…[6,58]). As far as the time optimal control of fluid flow models is concerned, the time optimal control problem for 2D NSE, Boussinesq equations, 3D Navier-Stokes-Voigt equations, 2D CBF equations with r ∈ [1,3], and 3D NS-α model is considered in [2,7,36,44,53], respectively. Stabilization of NSE is dealt to stabilize the equilibrium solution of NSE by using finite-dimensional feedback controllers having support either in interior or on the boundary of the domain (cf.…”

Section: Introductionmentioning

confidence: 99%

“…But the presence of the damping term |y| r−1 y helps us to obtain global results in 3D as well for supercritical CBF equations. The author in [44] discussed the time optimal control problem for 2D CBF equations with r ∈ [1, 3] by using a V-quantization and m-accretivity of the nonlinear operators. Hypothesis 2.2 and Proposition 3.5 help us to study the time optimal control problem of CBF equations for d ∈ {2, 3} with r > 3 also.…”

Section: Introductionmentioning

confidence: 99%

2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problems

Gautam,

Kinra,

Mohan

2024

MCRF

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The following convective Brinkman-Forchheimer (CBF) equations (or damped Navier-Stokes equations) with potential), we establish the existence of a unique global strong solution for the above multi-valued problem with the help of the abstract theory of maccretive operators. Moreover, we demonstrate that the same results hold local in time for the case d = 3 with r ∈ [1, 3) and d = r = 3 with 2βµ < 1. We explored the m-accretivity of the nonlinear as well as multi-valued operators, Yosida approximations and their properties, and several higher order energy estimates in the proofs. For r ∈ [1, 3], we quantize (modify) the Navier-Stokes nonlinearity (y • ∇)y to establish the existence and uniqueness results, while for r ∈ [3, ∞) (2βµ ≥ 1 for r = 3), we handle the Navier-Stokes nonlinearity by the nonlinear damping term β|y| r−1 y. Finally, we discuss the applications of the above developed theory in feedback control problems like flow invariance, time optimal control and stabilization.

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“…In [4] the author studied an optimal control problem constrained by the unsteady Stokes-Brinkman equation involving random data. For more models, we can refer to [5] [6].…”

Section: Introductionmentioning

confidence: 99%

Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations

Li¹

2023

ENG

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In this paper, we discuss virtual element method (VEM) approximation of optimal control problem governed by Brinkman equations with control constraints. Based on the polynomial projections and variational discretization of the control variable, we build up the virtual element discrete scheme of the optimal control problem and derive the discrete first order optimality system.A priori error estimates for the state, adjoint state and control variables in 2 L and 1 H norm are derived. The theoretical findings are illustrated by the numerical experiments.

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The Time Optimal Control of Two Dimensional Convective Brinkman–Forchheimer Equations

Cited by 4 publications

References 37 publications

Optimal control problems governed by two dimensional convective Brinkman-Forchheimer equations

Optimal control problems governed by two dimensional convective Brinkman-Forchheimer equations

2D and 3D convective Brinkman-Forchheimer equations perturbed by a subdifferential and applications to control problems

Virtual Element Discretization of Optimal Control Problem Governed by Brinkman Equations

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