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We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject…

Analysis of PDEs · Mathematics 2023-12-22 Thomas Eiter , Katharina Hopf , Robert Lasarzik

Under the action of a time-periodic external forces we prove the existence of at least one time-periodic weak solution for the interaction between a three-dimensional incompressible fluid, governed by the Navier- Stokes equation and a two…

Analysis of PDEs · Mathematics 2022-04-08 Claudiu Mîndrilă , Sebastian Schwarzacher

We consider a coupled PDE-ODE system describing the motion of the rigid body in a container filled with the incompressible, viscous fluid. The fluid and the rigid body are coupled via Navier slip boundary condition. We prove that the local…

Analysis of PDEs · Mathematics 2018-10-17 Nikolai V. Chemetov , Sarka Necasova , Boris Muha

In this paper, we study an interaction problem between a $3D$ compressible viscous fluid and a $3D$ nonlinear viscoelastic solid fully immersed in the fluid, coupled together on the interface surface. The solid is allowed to have…

Analysis of PDEs · Mathematics 2023-12-20 Malte Kampschulte , Boris Muha , Srđan Trifunović

We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn-Hilliard-type equation for two-phase flows and the Peterlin-Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2022-08-31 Aaron Brunk , Maria Lukacova-Medvidova

We study the question of weak solvability for a nonlinear coupled parabolic system that models the evolution of a complex pedestrian flow. The main feature is that the flow is composed of a mix of densities of active and passive pedestrians…

Analysis of PDEs · Mathematics 2019-10-14 T. K. Thoa Thieu , Matteo Colangeli , Adrian Muntean

We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a…

Analysis of PDEs · Mathematics 2019-06-05 Srđan Trifunović , Ya-Guang Wang

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 prove global existence of nonnegative weak solutions to a degenerate parabolic system which models the interaction of two thin fluid films in a porous medium. Furthermore, we show that these weak solutions converge at an exponential rate…

Analysis of PDEs · Mathematics 2011-10-31 Joachim Escher , Philippe Laurencot , Bogdan-Vasile Matioc

We study the discretisation of a uniaxial (rank-one) reduction of the Oldroyd-B model for dilute polymer solutions, in which the conformation tensor is represented as $\sig = \vec b \otimes \vec b$. Building on structural analogies with…

Numerical Analysis · Mathematics 2025-11-26 Ben S. Ashby , Gabriel R. Barrenechea , Alex Lukyanov , Tristan Pryer , Alex Trenam

We consider the Cauchy problem for incompressible viscoelastic fluids in the whole space $\mathbb{R}^d$ ($d=2,3$). By introducing a new decomposition via Helmholtz's projections, we first provide an alternative proof on the existence of…

Analysis of PDEs · Mathematics 2023-07-28 Xianpeng Hu , Hao Wu

We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one…

Analysis of PDEs · Mathematics 2015-06-01 Sergio Frigeri

We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model…

Analysis of PDEs · Mathematics 2015-06-03 Helmut Abels , Daniel Depner , Harald Garcke

We consider a coupled system of partial and ordinary differential equations describing the interaction between an isentropic inviscid fluid and a rigid body moving freely inside the fluid. We prove the existence of measure-valued solutions…

Analysis of PDEs · Mathematics 2022-06-07 Matteo Caggio , Ondřej Kreml , Šárka Nečasová , Arnab Roy , Tong Tang

We consider quasi-static poroelastic systems with incompressible constituents. The nonlinear permeability is taken to be dependent on solid dilation, and physical types of boundary conditions (Dirichlet, Neumann, and mixed) for the fluid…

Analysis of PDEs · Mathematics 2022-02-23 Lorena Bociu , Boris Muha , Justin T. Webster

In this paper, we prove the global existence of small smooth solutions to the three-dimensional incompressible Oldroyd-B model without damping on the stress tensor. The main difficulty is the lack of full dissipation in stress tensor. To…

Analysis of PDEs · Mathematics 2018-03-20 Yi Zhu

In this paper, we consider global strong solutions and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model in R^d, where d=2 and 3. The well-recognized problem of the global existence of smooth solutions for the 2D…

Analysis of PDEs · Mathematics 2024-10-15 Xinyu Cheng , Zhaonan Luo , Zhaojie Yang , Cheng Yuan

A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by [T. M. Elgindi, F. Rousset, Commun. Pure Appl. Math. 68 (2015), 2005--2021] where the global existence and uniqueness of the strong solution were established for…

Analysis of PDEs · Mathematics 2022-12-05 Yuanzhi Tu , Yinghui Wang , Huanyao Wen

We consider the evolution and interaction of a 2-dimensional nematic liquid crystal of Ericksen-Leslie type within a 1-dimensional flexible viscoelastic structure. This is a fully macroscopic model in which the nematic liquid crystal is…

Analysis of PDEs · Mathematics 2026-05-08 Prince Romeo Mensah

We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated…

Analysis of PDEs · Mathematics 2011-02-01 Ting Zhang , Daoyuan Fang