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We study controllability issues for the Navier-Stokes Equation on a two dimensional rectangle with so-called Lions boundary conditions. Rewriting the Equation using a basis of harmonic functions we arrive to an infinite-dimensional system…

Optimization and Control · Mathematics 2007-05-23 Sérgio Rodrigues

Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…

Analysis of PDEs · Mathematics 2023-06-14 Dennis Gallenmüller , Raphael Wagner , Emil Wiedemann

In this paper we study a coupled system modeling the movement of a deformable solid immersed in a fluid. For the solid we consider a given deformation that has to obey several physical constraints. The motion of the fluid is modeled by the…

Analysis of PDEs · Mathematics 2014-07-08 Sébastien Court

We prove a priori estimates for the system of partial differential equations modeling the interaction between an elastic body and an incompressible fluid in a 3D curved domain. The fluid is governed by the incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2026-01-21 B. Ingimarson , I. Kukavica , W. S. Ożański

In this paper we analyse the stability of the system of partial differential equations modelling scalar image velocimetry. We first revisit a successful numerical technique to reconstruct velocity vectors ${u}$ from images of a passive…

Analysis of PDEs · Mathematics 2020-08-24 E. Burman , J. J. J. Gillissen , L. Oksanen

The dynamic programming approach for the control of a 3D flow governed by the stochastic Navier-Stokes equations for incompressible fluid in a bounded domain is studied. By a compactness argument, existence of solutions for the associated…

Optimization and Control · Mathematics 2007-05-23 Luigi Manca

In this paper, we first investigate necessary optimality conditions for problems governed by systems describing the flow of an incompressible second grade fluid. Next, we study the asymptotic behavior of the optimal solution when the…

Optimization and Control · Mathematics 2016-01-21 Nadir Arada , Fernanda Cipriano

We report on the numerical implementation of thin film equations that describe the capillary-driven evolution of viscous films, in two-dimensional configurations. After recalling the general forms and features of these equations, we focus…

The paper is concerned with a class of mathematical models for polymeric fluids, which involves the coupling of the Navier-Stokes equations for a viscous, incompressible, constant-density fluid with a parabolic-hyperbolic…

Analysis of PDEs · Mathematics 2016-01-08 Miroslav Bulíček , Piotr Gwiazda , Endre Süli , Agnieszka Świerczewska-Gwiazda

We study the three-dimensional compressible Navier-Stokes equations coupled with the $Q$-tensor equation perturbed by a multiplicative stochastic force, which describes the motion of nematic liquid crystal flows. The local existence and…

Analysis of PDEs · Mathematics 2021-01-01 Yixuan Wang , Zhaoyang Qiu

A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic…

Analysis of PDEs · Mathematics 2022-12-06 Li Chen , Yue Li , Nicola Zamponi

We study a colocated cell centered finite volume method for the approximation of the incompressible Navier-Stokes equations posed on a 2D or 3D finite domain. The discrete unknowns are the components of the velocity and the pressures, all…

Numerical Analysis · Mathematics 2008-04-30 Robert Eymard , Raphaele Herbin , Jean-Claude Latché

The aim of this work is to analyze the finite element approximation of the two-dimensional stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes…

Numerical Analysis · Mathematics 2026-02-09 María Gabriela Armentano , Mauricio Mendiluce

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for…

Analysis of PDEs · Mathematics 2008-11-26 Hai-Liang Li , Jing Li , Zhouping Xin

In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…

Numerical Analysis · Mathematics 2023-08-08 Shafqat Ali , Francesco Ballarin , Gianluigi Rozza

Split form schemes for Euler and Navier-Stokes equations are useful for computation of turbulent flows due to their better robustness. This is because they satisfy additional conservation properties of the governing equations like kinetic…

Numerical Analysis · Mathematics 2021-05-03 Vikram Singh , Praveen Chandrashekar

We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…

Numerical Analysis · Mathematics 2007-05-23 Sebastien Zimmermann

This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity…

Analysis of PDEs · Mathematics 2016-12-26 Xin Liu

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…

Analysis of PDEs · Mathematics 2019-10-14 Sarka Necasova , Mythily Ramaswamy , Arnab Roy , Anja Schlomerkemper