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The flow of two macroscopically immiscible, viscous, incompressible fluids with unmatched densities is studied, where a transfer of mass between the constituents by phase transition is taken into account. To this end, two…

Analysis of PDEs · Mathematics 2025-05-09 Helmut Abels , Harald Garcke , Julia Wittmann

We study the Navier--Stokes equations governing the motion of an isentropic compressible fluid in three dimensions interacting with a flexible shell of Koiter type. The latter one constitutes a moving part of the boundary of the physical…

Analysis of PDEs · Mathematics 2018-01-17 Dominic Breit , Sebastian Schwarzacher

We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the…

Analysis of PDEs · Mathematics 2015-10-07 Yanjin Wang , Ian Tice , Chanwoo Kim

We investigate the dynamics of membranes that are held by freely-rotating tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. We characterize the oscillations…

Fluid Dynamics · Physics 2021-06-16 Christiana Mavroyiakoumou , Silas Alben

We consider the flow of a Newtonian fluid in a three-dimensional domain, rotating about a vertical axis and driven by a vertically invariant horizontal body-force. This system admits vertically invariant solutions that satisfy the 2D…

Fluid Dynamics · Physics 2023-07-19 Basile Gallet

In this paper, we consider a stationary, constant viscosity, incompressible Stokes flow with singular forces along one or several interfaces. Assuming only the jumps of the pressure are present along the interface, we develop a new…

Numerical Analysis · Mathematics 2009-11-26 K. S. Chang , D. Y. Kwak

The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the interface between two fluid phases. We first prove a priori…

Numerical Analysis · Mathematics 2020-04-23 Ernesto Cáceres , Johnny Guzmán , Maxim Olshanskii

A semi-explicit formula of solution to the boundary layer system for thermal layer derived from the compressible Navier-Stokes equations with the non-slip boundary condition when the viscosity coefficients vanish is given, in particular in…

Analysis of PDEs · Mathematics 2016-08-10 Cheng-Jie Liu , Ya-Guang Wang , Tong Yang

We prove that, in a two-dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half-plane. The…

Analysis of PDEs · Mathematics 2015-09-16 François Hamel , Nikolai Nadirashvili

We consider a nonlinear, free boundary fluid-structure interaction model in a bounded domain. The viscous incompressible fluid interacts with a nonlinear elastic body on the common boundary via the velocity and stress matching conditions.…

Analysis of PDEs · Mathematics 2018-02-05 Yizhao Qin , Pengfei Yao

We investigate the sharp interface limit of a diffuse interface system that couples the Allen--Cahn equation with the instationary Navier--Stokes system in a bounded domain in $\mathbb{R}^d$ with $d \in \{2,3\}$. This model is used to…

Analysis of PDEs · Mathematics 2022-05-17 Sebastian Hensel , Yuning Liu

The Stokes equation with the varying viscosity is considered in a thin tube structure, i.e. in a connected union of thin rectangles with heights of order $\varepsilon<<1 $ and with bases of order 1 with smoothened boundary. An asymptotic…

Analysis of PDEs · Mathematics 2014-03-25 G. Cardone , R. Fares , G. P. Panasenko

We introduce a diffuse interface model describing the evolution of a mixture of two different viscous incompressible fluids of equal density. The main novelty of the present contribution consists in the fact that the effects of temperature…

Analysis of PDEs · Mathematics 2014-01-15 Michela Eleuteri , Elisabetta Rocca , Giulio Schimperna

Having a finite interfacial thickness, the phase-field models supply a way to model the fluid interfaces, which allows the calculations of the interface movements and deformations on the fixed grids. Such modeling is applied to the…

Analysis of PDEs · Mathematics 2024-07-24 Nitu Lakhmara , Hari Shankar Mahato

In this work, we derive a result of exponential stability for a coupled system of partial differential equations (PDEs) which governs a certain fluid-structure interaction. In particular, a three-dimensional Stokes flow interacts across a…

Analysis of PDEs · Mathematics 2014-03-26 George Avalos , Francesca Bucci

The study solves the general solution to 2D steady Navier-Stokes equation for incompressible flow without vorticity diffusion, which is more general than Stokes flow. In order to obtain the general solution, two potential functions are…

Fluid Dynamics · Physics 2023-01-11 Peng Shi

In [Lacave, IHP, ana, to appear (2008)] the author considered the two dimensional Euler equations in the exterior of a thin obstacle shrinking to a curve and determined the limit velocity. In the present work, we consider the same problem…

Analysis of PDEs · Mathematics 2009-02-13 Christophe Lacave

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes…

Analysis of PDEs · Mathematics 2016-02-17 C. Grandmont , M. Hillairet

We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier-Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With…

Analysis of PDEs · Mathematics 2022-08-24 Sebastian Hensel , Alice Marveggio

Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…

Mathematical Physics · Physics 2024-08-20 Maik Porrmann , Axel Voigt