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This paper is concerned with the mathematical analysis of time-dependent fluid-solid interaction problem associated with a bounded elastic body immersed in a homogeneous air or fluid above a local rough surface. We reformulate the unbounded…

Analysis of PDEs · Mathematics 2018-07-25 Changkun Wei , Jiaqing Yang

We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the Stokes equations, from a single measurement of force and velocity on a portion of the boundary. We obtain…

Analysis of PDEs · Mathematics 2015-05-18 Andrea Ballerini

Stokes flows with near-touching rigid particles induce near-singular lubrication forces under relative motion, making their accurate numerical treatment challenging. With the aim of controlling the accuracy with a computationally cheap…

Numerical Analysis · Mathematics 2024-11-26 Anna Broms , Alex H. Barnett , Anna-Karin Tornberg

We develop mathematical methods which allow us to study asymptotic properties of solutions to the three dimensional Navier-Stokes system for incompressible fluid in the whole three dimensional space. We deal either with the Cauchy problem…

Analysis of PDEs · Mathematics 2020-12-24 Marco Cannone , Grzegorz Karch , Dominika Pilarczyk , Gang Wu

We consider the modified Navier-Stokes equations in R3 describing the motion of a fluid in the presence of a rotating rigid body. Weighted Sobolev spaces are used to describe the behavior of solutions at large distances. Under suitable…

Analysis of PDEs · Mathematics 2026-01-09 Tahar Zamène Boulmezaoud , Nabil Kerdid , Amel Kourta

We present an exact solution for the time-dependent Stokes problem of an infinite cylinder of radius r=a in a fluid with harmonic boundary conditions at infinity. This is a 3-dimensional problem but, because of translational invariance…

Mathematical Physics · Physics 2008-04-14 Andreas N. Vollmayr , Jan-Moritz P. Franosch , J. Leo van Hemmen

The stationary Navier-Stokes equations for a non-Newtonian incompressible fluid are coupled with the stationary heat equation and subject to Dirichlet type boundary conditions. The viscosity is supposed to depend on the temperature and the…

Analysis of PDEs · Mathematics 2025-01-27 Maurizio Grasselli , Nicola Parolini , Andrea Poiatti , Marco Verani

Lubrication theory makes use of the assumptions of a long and thin fluid domain and a small scaled Reynolds number to formulate a linearized approximation to the Navier-Stokes equations. Extended lubrication theory aims to improve the model…

Fluid Dynamics · Physics 2026-03-05 Sarah Dennis , Thomas G. Fai

The three-dimensional jump conditions for the pressure and velocity fields, up to the second normal derivative,across an incompressible/inextensible interface in the Stokes regime are derived herein. The fluid viscosity is only piecewise…

Fluid Dynamics · Physics 2013-09-09 Prerna Gera , David Salac

In this paper we study the motion of a rigid body driven by Newton's law immersed in a stationary incompressible Stokes flow occupying a bounded simply connected domain. The aim is that of trajectory tracking of the solid by the means of a…

Analysis of PDEs · Mathematics 2022-03-01 József J. Kolumbán

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 the well-posedness of a system of partial differential equations that model the dynamics of a two-dimensional Stokes bubble immersed in two-dimensional ambient Stokes fluid of the same viscosity that extends to…

Analysis of PDEs · Mathematics 2024-06-13 Jae Ho Choi

A non-conventional shape optimization approach is introduced to address the identification of an obstacle immersed in a fluid described by the Stokes equation within a larger bounded domain, relying on boundary measurements on the…

Optimization and Control · Mathematics 2024-03-19 Julius Fergy Tiongson Rabago , Lekbir Afraites , Hirofumi Notsu

We study a stationary 3D/2D fluid-structure interaction problem between an elastic structure described by the linear plate equation and a fluid described by the compressible Navier-Stokes equations with hard-sphere pressure and…

Analysis of PDEs · Mathematics 2026-03-30 Boris Muha , Šárka Nečasová , Milan Pokorný , Srđan Trifunović , Justin T. Webster

We solve the Stokes equations for the flow around two parallel translating and rotating cylinders using tools from complex analysis and conformal mapping. By considering cylinders of arbitrary size and separation, we generalise the…

Fluid Dynamics · Physics 2025-02-11 Luke Neville

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

In this paper, we are first interested in the compressible Navier-Stokes equations with densitydependent viscosities in bounded domains with on-homogeneous Dirichlet conditions. We study the wellposedness of such models with non-constant…

Analysis of PDEs · Mathematics 2009-06-09 Laurent Chupin , Rémy Sart

We study the asymptotic behavior of an incompressible fluid around a bounded obstacle. The problem is modeled by the stationary Navier-Stokes equations in an exterior domain in $\R^n$ with $n\ge 2$. We will show that, under some…

Analysis of PDEs · Mathematics 2010-08-25 Ching-Lung Lin , Gunther Uhlmann , Jenn-Nan Wang

A thermal convection flow in the three-dimensional unbounded fluid domain exterior to a sphere is considered. The viscosity force is determined by a fractional power of the Stokes operator. A purely conductive steady state arises due to the…

Analysis of PDEs · Mathematics 2026-05-14 Zhi-Min Chen

In this paper we analyze the finite element approximation of the Stokes equations with non-smooth Dirichlet boundary data. To define the discrete solution, we first approximate the boundary datum by a smooth one and then apply a standard…

Numerical Analysis · Mathematics 2019-12-12 Ricardo G. Durán , Lucia Gastaldi , Ariel L. Lombardi