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We consider the flow of a viscous, incompressible, Newtonian fluid in a perforated domain in the plane. The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and…

Analysis of PDEs · Mathematics 2015-08-31 Christophe Lacave , Anna Mazzucato

In this article, we consider Leray solutions of the Navier-Stokes equations in the exterior of one obstacle in 3D and we study the asymptotic behavior of these solutions when the obstacle shrinks to a curve or to a surface. In particular,…

Analysis of PDEs · Mathematics 2013-06-21 Christophe Lacave

We consider the motion of a rigid body, governed by the Navier-Stokes equations in a bounded domain. Navier's condition is prescribed on the boundary of the body. We give the global in a time solvability result of weak solution. The result…

Analysis of PDEs · Mathematics 2017-06-20 Nikolai V. Chemetov , Sarka Necasova

Assuming that initial velocity and initial vorticity are bounded in the plane, we show that on a sufficiently short time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the Euler…

Analysis of PDEs · Mathematics 2008-08-27 Elaine Cozzi

We show that the collective effect of $N$ rigid bodies $(\mathcal{S}_{n,N})_{n=1}^N$ of diameters $(r_{n,N})_{n=1}^N$ immersed in an incompressible non--Newtonian fluid is negligible in the asymptotic limit $N \to \infty$ as long as their…

Analysis of PDEs · Mathematics 2024-04-11 Eduard Feireisl , Arnab Roy , Arghir Zarnescu

Let $\mathcal B$ be a sufficiently smooth rigid body (compact set of $\mathbb R^3$) of arbitrary shape moving in an unbounded Navier-Stokes liquid under the action of prescribed external force, $\textup{F}$, and torque, $\textup{M}$. We…

Analysis of PDEs · Mathematics 2023-05-31 Giovanni P. Galdi

In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…

Analysis of PDEs · Mathematics 2009-02-17 D. Iftimie , M. C. Lopes Filho , H. J. Nussenzveig Lopes

Assuming that initial velocity has finite energy and initial vorticity is bounded in the plane, we show that for any finite time interval the unique solutions of the Navier-Stokes equations converge uniformly to the unique solution of the…

Analysis of PDEs · Mathematics 2009-03-27 Elaine Cozzi

We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. Assuming the object is a ball of a small radius $\varepsilon$ we show that the behavior of the fluid is not…

Analysis of PDEs · Mathematics 2022-08-18 Eduard Feireisl , Arnab Roy , Arghir Zarnescu

We consider the fluid-structure interaction problem of a viscous incompressible fluid contained in an elastic solid whose motion is not prescribed. The equations governing the motion of the solid are given by the Navier equations of linear…

Analysis of PDEs · Mathematics 2025-07-01 Giusy Mazzone

We consider the interaction of a compressible fluid with a flexible plate in two space dimensions. The fluid is described by the Navier--Stokes equations in a domain that is changing in accordance with the motion of the structure. The…

Analysis of PDEs · Mathematics 2024-11-05 Dominic Breit , Arnab Roy

The aim of this work is to study the Navier-Stokes-Voigt equations that govern flows with non-negative density of incompressible fluids with elastic properties. For the associated non-linear initial-and boundary-value problem, we prove the…

Analysis of PDEs · Mathematics 2023-09-04 Hermenegildo Borges de Oliveira , Khonatbek Khompysh , Aidos Ganizhanuly Shakir

A rigid body, with an interior cavity entirely filled with a Navier-Stokes liquid, moves in absence of external torques relative to the center of mass of the coupled system body-liquid (inertial motions). The only steady-state motions…

Analysis of PDEs · Mathematics 2017-05-12 Giovanni P. Galdi

In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the domain. This is…

Analysis of PDEs · Mathematics 2021-03-17 S. Necasova , M. Ramaswamy , A. Roy , A. Schlomerkemper

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in…

Analysis of PDEs · Mathematics 2015-05-28 Matthieu Hillairet , Peter Wittwer

In this work we study the coupled system of partial and ordinary differential equations describing the interaction between a compressible isentropic viscous fluid and a rigid body moving freely inside the fluid. In particular the position…

Analysis of PDEs · Mathematics 2019-05-27 Ondrej Kreml , Sarka Necasova , Tomasz Piasecki

In the present paper we study the fast rotation limit for viscous incompressible fluids with variable density, whose motion is influenced by the Coriolis force. We restrict our analysis to two dimensional flows. In the case when the initial…

Analysis of PDEs · Mathematics 2017-07-04 Francesco Fanelli , Isabelle Gallagher

We consider the inertial motion of a system constituted by a rigid body with an interior cavity entirely filled with a viscous incompressible fluid. Navier boundary conditions are imposed on the cavity surface. We prove the existence of…

Analysis of PDEs · Mathematics 2018-09-12 Giusy Mazzone , Jan Pruess , Gieri Simonett

We study the motion of the system, S, constituted by a rigid body, B, containing in its interior a viscous compressible fluid, and moving in absence of external forces. Our main objective is to characterize the long time behavior of the…

Analysis of PDEs · Mathematics 2019-01-30 Giovanni Paolo Galdi , Václav Mácha , Šárka Nečasová

We consider the motion of a rigid body immersed in an ideal flow occupying the plane, with bounded initial vorticity. In that case there exists a unique corresponding solution which is global in time, in the spirit of the famous work by…

Analysis of PDEs · Mathematics 2024-12-30 Olivier Glass , Franck Sueur