English
Related papers

Related papers: Stabilization of a fluid-solid system, by the defo…

200 papers

We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a…

Analysis of PDEs · Mathematics 2021-08-12 Pei Su , Marius Tucsnak

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary…

Analysis of PDEs · Mathematics 2017-10-25 Yan Guo , Ian Tice

In this article we study the local stabilization of the non-homogeneous Navier- Stokes equations in a 2d channel around Poiseuille flow. We design a feedback control of the velocity which acts on the inflow boundary of the domain such that…

Analysis of PDEs · Mathematics 2018-07-12 Sourav Mitra

In this article, we study the strong well-posedness, stability and optimal control of an incompressible magneto-viscoelastic fluid model in two dimensions. The model consists of an incompressible Navier--Stokes equation for the velocity…

Analysis of PDEs · Mathematics 2021-08-09 Harald Garcke , Patrik Knopf , Sourav Mitra , Anja Schlömerkemper

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic solid shell. The fluid motion is governed by the Navier-Stokes equations, while the shell is modeled by…

Analysis of PDEs · Mathematics 2007-05-23 C. H. Arthur Cheng , Daniel Coutand , Steve Shkoller

We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…

Analysis of PDEs · Mathematics 2024-10-25 Yuanzhen Shao , Gieri Simonett , Mathias Wilke

A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…

Classical Physics · Physics 2025-06-26 D. Bigoni , S. G. Mogilevskaya , A. Piccolroaz , M. Gaibotti

It is an outstanding problem whether a pipe-flow system on a star-shaped network is stabilisable by a feedback control on the common vertex. In the present paper we deal with this problem. In particular, we study the equation governing the…

Analysis of PDEs · Mathematics 2024-07-26 Xiao Xuan Feng , Gen Qi Xu , Mahyar Mahinzaeim

We study the behaviour of circular flexible loops sedimenting in a viscous fluid by numerical simulations and linear stability analysis. The numerical model involves a local slender-body theory approximation for the flow coupled to the…

Fluid Dynamics · Physics 2021-07-01 Radost Waszkiewicz , Piotr Szymczak , Maciej Lisicki

We consider the strong stabilization of small amplitude gravity water waves in a two dimensional rectangular domain. The control acts on one lateral boundary, by imposing the horizontal acceleration of the water along that boundary, as a…

Analysis of PDEs · Mathematics 2020-03-24 Pei Su , Marius Tucsnak , George Weiss

In a recent work [1] the authors studied the dynamics of the interface separating a vacuum from an inviscid incompressible fluid, subject to the self-gravitational force and neglecting surface tension, in two space dimensions. The fluid is…

Analysis of PDEs · Mathematics 2015-11-25 Lydia Bieri , Shuang Miao , Sohrab Shahshahani , Sijue Wu

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

Systems and Control · Computer Science 2017-04-26 H. Jardon-Kojakhmetov , Jacquelien M. A. Scherpen , D. del Puerto-Flores

We study a three-dimensional fluid-structure interaction problem describing the motion of an incompressible, viscous fluid coupled with a deformable elastic shell of Koiter type that forms part of the fluid boundary. The fluid motion is…

Analysis of PDEs · Mathematics 2026-02-24 Claudiu Mîndrilă , Arnab Roy

In this article, we study the long-time behavior of solutions of the two-dimensional fluid-rigid disk problem. The motion of the fluid is modeled by the two-dimensional Navier-Stokes equations, and the disk moves under the influence of the…

Analysis of PDEs · Mathematics 2015-06-12 Sylvain Ervedoza , Matthieu Hillairet , Christophe Lacave

We study a novel approach for the existence of solutions to an incompressible fluid-rigid body interaction problem in three dimensions. Our approach introduces an iteration based on a sequence of related problems posed on domains with…

Numerical Analysis · Mathematics 2026-01-21 Charles M. Elliott , Thomas Sales

The stability of a three-dimensional, incompressible, viscous flow through a finite-length duct is studied. A divergence-free basis technique is used to formulate the weak form of the problem. A SUPG (streamingline upwind Petrov-Galerkin)…

Fluid Dynamics · Physics 2019-08-07 Lei Xu , Zvi Rusak

The so-called 'direct' approach to separation of variables in linear PDEs is applied to the hydrodynamic stability problem. Calculations are made for the complete linear stability equations in cylindrical coordinates. Several classes of the…

Fluid Dynamics · Physics 2007-05-23 Georgy Burde , Alexander Zhalij

This paper presents a complete inverse optimality study for a linearized tank-liquid system where the liquid is described by the viscous Saint-Venant model with surface tension and possible wall friction. We define an appropriate weak…

Optimization and Control · Mathematics 2024-05-28 Iasson Karafyllis , Filippos Vokos , Miroslav Krstic

In this paper, we study a hydrodynamic system modeling the deformation of vesicle membranes in incompressible viscous fluids. The system consists of the Navier-Stokes equations coupled with a fourth order phase-field equation. In the three…

Analysis of PDEs · Mathematics 2013-02-26 Hao Wu , Xiang Xu

This paper concerns the construction of traveling wave solutions to the free boundary incompressible Navier-Stokes system. We study a single layer of viscous fluid in a strip-like domain that is bounded below by a flat rigid surface and…

Analysis of PDEs · Mathematics 2022-09-13 Junichi Koganemaru , Ian Tice