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We consider the large time behavior of the three-dimensional Navier-Stokes flow around a rotating rigid body. Assume that the angular velocity of the body gradually increases until it reaches a small terminal one at a certain finite time…

Analysis of PDEs · Mathematics 2020-10-06 T. Takahashi

We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\Omega \subset \mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion…

Analysis of PDEs · Mathematics 2024-08-15 Šimon Axmann , Šárka Nečasová , Ana Radošević

We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows…

Analysis of PDEs · Mathematics 2020-03-18 Giovanni Paolo Galdi , Václav Mácha , Šárka Nečasová

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter $\ep \to 0$ and the fluid is confined to an exterior spatial domain $\Omega_\ep$ that may vary with…

Analysis of PDEs · Mathematics 2015-04-01 Eduard Feireisl , Trygve K. Karper , Ondrej Kreml , Jan Stebel

A body $\mathscr B$ moves in an unbounded Navier-Stokes liquid by time-independent translatory motion. Suppose that at time $t=0$, $\mathscr B$ smoothly changes its motion to an arbitrary rigid motion, reached at time $t=1$. We then show…

Analysis of PDEs · Mathematics 2026-05-08 Giovanni P. Galdi , Toshiaki Hishida

We consider the motion of several solids in a bounded cavity filled with a perfect incompressible fluid, in two dimensions. The solids move according to Newton's law, under the influence of the fluid's pressure, and the fluid dynamics is…

Analysis of PDEs · Mathematics 2019-10-09 Olivier Glass , Franck Sueur

The issue of the inviscid limit for the incompressible Navier-Stokes equations when a no-slip condition is prescribed on the boundary is a famous open problem. A result by Tosio Kato says that convergence to the Euler equations holds true…

Analysis of PDEs · Mathematics 2015-05-30 Franck Sueur

We study a 3D fluid-rigid body interaction problem. The fluid flow is governed by 3D incompressible Navier-Stokes equations, while the motion of the rigid body is described by a system of ordinary differential equations describing…

Analysis of PDEs · Mathematics 2023-07-07 Boris Muha , Šárka Nečasová , Ana Radošević

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

We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…

Analysis of PDEs · Mathematics 2021-12-15 Toshiaki Hishida , Mads Kyed

The existence of weak solutions to the "viscous incompressible fluid + rigid body" system with Navier slip-with-friction conditions in a 3D bounded domain has been recently proved by G\'{e}rard-Varet and Hillairet in \cite{exi:GeH}. In 2D…

Analysis of PDEs · Mathematics 2019-05-01 Marco Bravin

We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier-Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain…

Analysis of PDEs · Mathematics 2009-11-13 David Gérard-Varet , Matthieu Hillairet

We investigate the steady self-propelled motion of a rigid body immersed in a three-dimensional incompressible viscous fluid governed by the Navier-Stokes equations. The analysis is performed in a body-fixed reference frame, so that the…

Analysis of PDEs · Mathematics 2026-01-01 Sarka Necasova , Arnab Roy , Ana Leonor Silvestre

We consider the physical setup of a three-dimensional fluid-structure interaction problem. A viscous compressible gas or liquid interacts with a nonlinear, visco-elastic, three-dimensional bulk solid. The latter is described by a hyperbolic…

Analysis of PDEs · Mathematics 2021-08-09 Dominic Breit , Malte Kampschulte , Sebastian Schwarzacher

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

We develop the asymptotic behavior for the solutions to the stationary Navier-Stokes equation in the exterior domain of the 2D hyperbolic space. More precisely, given the finite Dirichlet norm of the velocity, we show the velocity decays to…

Analysis of PDEs · Mathematics 2017-05-25 Chi Hin Chan , Che-Kai Chen , Magdalena Czubak

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 paper, we are concerned with the global well-posedness of 3D inhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity when the initial velocity is sufficiently small in the critical Besov space…

Analysis of PDEs · Mathematics 2024-01-19 Dongjuan Niu , Lu Wang

We consider the system constituted by a hollow rigid body whose cavity contains a homogeneous rigid ball, and let the gap between the solids be entirely filled by a viscous incompressible fluid. We investigate the free rotations of the…

Analysis of PDEs · Mathematics 2020-11-30 Giusy Mazzone

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