Bilinear Optimal Control Problem for the Stationary Navier–Stokes Equations with Variable Density and Slip Boundary Condition

Mallea-Zepeda, Exequiel; Lenes, Eber; Zambrano, Jonnathan Rodríguez

doi:10.1007/s00574-019-00131-6

Cited by 3 publications

(3 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To define the concept of weak solutions of problem NS-MBC, following the ideas of Frolov [16] (see, also [17][18][19][20][21], for more details), we express the fluid density in terms of the stream function. Namely, assuming conditions (4) and ( 5), we can express the fluid density as follows:…”

Section: Weak Solutionsmentioning

confidence: 99%

“…This representation allows us to drop the continuity equation, which facilitates the introduction of the weak solution concept of problem NS-MBC. The stream formulation was used in [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…He investigated optimal boundary control for a model of 2D steady-state flows of a nonhomogeneous incompressible fluid under the assumption that the viscosity µ is constant. Using the external forces field as a control function, Mallea-Zepeda et al [19] proved the existence of optimal solutions to this model and obtained the first-order necessary optimality conditions. Boundary control for a 2D stationary system of micropolar fluid with variable density was studied in [20].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Control Problem Related to 2D Stokes Equations with Variable Density and Viscosity

et al. 2021

Self Cite

View full text Add to dashboard Cite

We study an optimal control problem for the stationary Stokes equations with variable density and viscosity in a 2D bounded domain under mixed boundary conditions. On in-flow and out-flow parts of the boundary, nonhomogeneous Dirichlet boundary conditions are used, while on the solid walls of the flow domain, the impermeability condition and the Navier slip condition are provided. We control the system by the external forces (distributed control) as well as the velocity boundary control acting on a fixed part of the boundary. We prove the existence of weak solutions of the state equations, by firstly expressing the fluid density in terms of the stream function (Frolov formulation). Then, we analyze the control problem and prove the existence of global optimal solutions. Using a Lagrange multipliers theorem in Banach spaces, we derive an optimality system. We also establish a second-order sufficient optimality condition and show that the marginal function of this control system is lower semi-continuous.

show abstract

Section: Weak Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Control Problem Related to 2D Stokes Equations with Variable Density and Viscosity

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

Mathematical modeling and numerical multigoal-oriented a posteriori error control and adaptivity for a stationary, nonlinear, coupled flow temperature model with temperature dependent density

Beuchler,

Demircan,

Endtmayer

et al. 2024

Computers & Mathematics with Applications

View full text Add to dashboard Cite

A 3D Non-Stationary Micropolar Fluids Equations with Navier Slip Boundary Conditions

2021

View full text Add to dashboard Cite

Micropolar fluids are fluids with microstructure and belong to a class of fluids with asymmetric stress tensor that called Polar fluids, and include, as a special case, the well-established Navier–Stokes model. In this work we study a 3D micropolar fluids model with Navier boundary conditions without friction for the velocity field and homogeneous Dirichlet boundary conditions for the angular velocity. Using the Galerkin method, we prove the existence of weak solutions and establish a Prodi–Serrin regularity type result which allow us to obtain global-in-time strong solutions at finite time.

show abstract

Bilinear Optimal Control Problem for the Stationary Navier–Stokes Equations with Variable Density and Slip Boundary Condition

Cited by 3 publications

References 29 publications

Control Problem Related to 2D Stokes Equations with Variable Density and Viscosity

Control Problem Related to 2D Stokes Equations with Variable Density and Viscosity

Mathematical modeling and numerical multigoal-oriented a posteriori error control and adaptivity for a stationary, nonlinear, coupled flow temperature model with temperature dependent density

A 3D Non-Stationary Micropolar Fluids Equations with Navier Slip Boundary Conditions

Contact Info

Product

Resources

About