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In this paper we consider a fluid-structure interaction problem given by the steady Navier Stokes equations coupled with linear elasticity taken from [Lasiecka, Szulc, and Zochoswki, Nonl. Anal.: Real World Appl., 44, 2018]. An elastic body…

Optimization and Control · Mathematics 2021-09-07 Michael Hintermüller , Axel Kröner

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in $\R^3$ with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the…

Analysis of PDEs · Mathematics 2009-01-05 Gui-Qiang Chen , Zhongmin Qian

This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain…

Optimization and Control · Mathematics 2007-05-23 Z. M. Gao , Y. C. Ma , H. W. Zhuang

In this paper we study obstacles immerged in a Stokes flow with Navier boundary conditions. We prove the existence and regularity of an obstacle with minimal drag, among all shapes of prescribed volume and controlled surface area, taking…

Analysis of PDEs · Mathematics 2023-01-04 Dorin Bucur , Antonin Chambolle , Alessandro Giacomini , Mickaël Nahon

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…

Numerical Analysis · Mathematics 2017-07-12 Sébastien Court , Michel Fournié

In this work we study an optimal control problem subject to the instationary Navier-Stokes equations, where the control enters via an inhomogeneous Neumann/Do-Nothing boundary condition. Despite the Navier-Stokes equations with these…

Optimization and Control · Mathematics 2026-05-20 Boris Vexler , Jakob Wagner

This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can…

Computational Physics · Physics 2020-05-18 Yongbo Deng , Weihong Zhang , Jihong Zhu , Junqiang Bai , Zhenyu Liu , Jan G. Korvink

We consider a velocity tracking problem for stochastic Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through an injection-suction device with uncertainty, which acts in accordance with the non-homogeneous…

Probability · Mathematics 2024-09-04 Nikolai Chemetov , Fernanda Cipriano

This article presents a new boundary integral approach for finding optimal shapes of peristaltic pumps that transport a viscous fluid. Formulas for computing the shape derivatives of the standard cost functionals and constraints are…

Optimization and Control · Mathematics 2019-03-12 Marc Bonnet , Ruowen Liu , Shravan Veerapaneni

We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the…

Optimization and Control · Mathematics 2014-07-22 Harald Garcke , Claudia Hecht

In this paper, we study the role of boundary conditions on the optimal shape of a dyadic tree in which flows a Newtonian fluid. Our optimization problem consists in finding the shape of the tree that minimizes the viscous energy dissipated…

Analysis of PDEs · Mathematics 2010-12-13 Xavier Dubois De La Sablonière , Benjamin Mauroy , Yannick Privat

Spaces where each element describes a shape, so-called shape spaces, are of particular interest in shape optimization and its applications. Theory and algorithms in shape optimization are often based on techniques from differential…

Optimization and Control · Mathematics 2025-04-01 Lidiya Pryymak , Tim Suchan , Kathrin Welker

Nonlinear convection, the source of turbulence in fluid flows, may hold the key to stabilizing turbulence by solving a specific cubic polynomial equation. We consider the incompressible Navier-Stokes equations in a two-dimensional channel.…

Systems and Control · Electrical Eng. & Systems 2024-09-27 Mohamed Camil Belhadjoudja , Miroslav Krstic , Emmanuel Witrant

We consider a velocity tracking problem for the Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through a injection-suction device and the flow is allowed to slip against the surface wall. We study the…

Analysis of PDEs · Mathematics 2017-06-20 Nikolai V. Chemetov , Fernanda Cipriano

This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a…

Optimization and Control · Mathematics 2021-10-05 Marc Bonnet , Ruowen Liu , Shravan Veerapaneni , Hai Zhu

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…

Analysis of PDEs · Mathematics 2009-01-05 Gui-Qiang Chen , Dan Osborne , Zhongmin Qian

WE PRESENT THE RANDOM REPRESENTATIONS FOR THE NAVIER-STOKES VORTICITY EQUATIONS FOR AN INCOMPRESSIBLE FLUID IN A SMOOTH MANIFOLD WITH BOUNDARY AND REFLECTING BOUNDARY CONDITIONS FOR THE VORTICITY. WE SPECIALIZE OUR CONSTRUCTIONS TO…

Mathematical Physics · Physics 2007-05-23 Diego L. Rapoport

We study well-posedness of a velocity-vorticity formulation of the Navier--Stokes equations, supplemented with no-slip velocity boundary conditions, a no-penetration vorticity boundary condition, along with a natural vorticity boundary…

Analysis of PDEs · Mathematics 2017-08-09 Maxim A. Olshanskii , Leo G. Rebholz , Abner J. Salgado

The steady motion of a viscous incompressible fluid in distorted pipes, of finite length, is modeled through the Navier-Stokes equations with mixed boundary conditions: the inflow is given by an arbitrary member of the Lions-Magenes class…

Analysis of PDEs · Mathematics 2025-06-10 Alessio Falocchi , Ana Leonor Silvestre , Gianmarco Sperone

Consider a rigid body ${\mathcal S} \subset {\mathbb R}^3$ immersed in an infinitely extended Navier-Stokes liquid and the motion of the body-fluid interaction system described from a reference frame attached to ${\mathcal S}$. We are…

Analysis of PDEs · Mathematics 2020-03-10 Toshiaki Hishida , Ana Leonor Silvestre , Takéo Takahashi