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We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the motion of the rigid body is described by the…

Analysis of PDEs · Mathematics 2021-03-10 Jiao He , Dragos Iftimie

In this paper we study the dynamics of an incompressible viscous fluid evolving in an open-top container in two dimensions. The fluid mechanics are dictated by the Navier-Stokes equations. The upper boundary of the fluid is free and evolves…

Analysis of PDEs · Mathematics 2020-10-30 Yan Guo , Ian Tice

We study the three-dimensional compressible elastic Navier-Stokes-Poisson equations induced by a new bipolar viscoelastic model derived here, which model the motion of the compressible electrically conducting fluids. The various boundary…

Analysis of PDEs · Mathematics 2023-06-07 Wenpei Wu , Yong Wang

A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The…

Analysis of PDEs · Mathematics 2023-02-23 Tomáš Roubíček

In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…

Analysis of PDEs · Mathematics 2016-07-15 Šimon Axmann , Piotr B. Mucha , Milan Pokorný

We study an incompressible viscous flow around an obstacle with an oscillating boundary that moves by a translational periodic motion, and we show existence of strong time-periodic solutions for small data in different configurations: If…

Analysis of PDEs · Mathematics 2023-03-20 Thomas Eiter , Yoshihiro Shibata

We study the interaction between incompressible viscous fluids and multilayered elastic structures in a 3D/2D/3D framework, where a 3D fluid interacts with a 2D thin elastic layer, coupled to a 3D thick elastic solid. The system is driven…

Analysis of PDEs · Mathematics 2025-01-14 Claudiu Mîndrilă , Arnab Roy

We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by…

Analysis of PDEs · Mathematics 2025-11-18 Helmut Abels , Alice Marveggio , Andrea Poiatti

Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids,…

Analysis of PDEs · Mathematics 2021-08-31 Tomáš Roubíček

We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in…

Analysis of PDEs · Mathematics 2024-02-15 Gael Y. Diebou

We study the nonhomogeneous boundary value problem for Navier-Stokes equations of steady motion of a viscous incompressible fluid in a three-dimensional bounded multiply connected domain. We prove that this problem has a solution in some…

Mathematical Physics · Physics 2012-04-12 Mikhail Korobkov , Konstantin Pileckas , Remigio Russo

We prove the existence of time-periodic weak solutions for a fluid-structure interaction system coupling the incompressible Navier-Stokes equations in a three-dimensional moving domain with a nonlinear Koiter plate equation on its upper…

Analysis of PDEs · Mathematics 2026-05-20 Claudiu Mîndrilă

In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial…

Fluid Dynamics · Physics 2022-08-23 Wennan Zou

We develop a combined field formulation for the fluid structure (FS) interaction problem. The unknowns are (u;p;v), being the fluid velocity, fluid pressure and solid velocity. This combined field formulation uses Arbitrary Lagrangian…

Numerical Analysis · Mathematics 2014-01-03 Jie Liu

The motion of a thin elastic plate interacting with a viscous fluid is investigated. A periodic force acting on the plate is considered, which in a setting without damping could lead to a resonant response. The interaction with the viscous…

Analysis of PDEs · Mathematics 2021-03-02 Aday Celik , Mads Kyed

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

The three-dimensional, homogeneous, incompressible Navier-Stokes equations are studied in the absence of viscosity in one direction. It is shown that there are arbitrarily large initial data generating a unique global solution, the main…

Analysis of PDEs · Mathematics 2022-02-24 Isabelle Gallagher , Alexandre Yotopoulos

Consider an exterior space-time domain where the incompressible Navier-Stokes equation and continuity equation hold with no bodies or force fields present, and smooth velocity at initial time. This is equivalent to the velocity being…

Analysis of PDEs · Mathematics 2023-05-24 Edmund Chadwick

This paper investigates the global dynamics of a three-dimensional fluid-particle interaction system that couples the compressible barotropic Navier-Stokes equations with the Vlasov-Fokker-Planck equation through a density-dependent…

Analysis of PDEs · Mathematics 2026-03-10 Fucai Li , Jinkai Ni , Dehua Wang

Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent fluid flows where they often emerge on time-scales much shorter than the viscous time scale, and then dominate the dynamics for very long time…

Analysis of PDEs · Mathematics 2012-05-18 Margaret Beck , C. Eugene Wayne