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Related papers: Global Well-Posedness for 2-D Viscoelastic Fluid M…

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We prove the existence of weak solutions and a unique strong solution to the Oldroyd-B dumbbell model describing the evolution of a two-dimensional dilute polymer fluid interacting with a one-dimensional viscoelastic shell. The polymer…

Analysis of PDEs · Mathematics 2025-06-13 Prince Romeo Mensah

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

We provide a proof of global regularity of solutions of some models of viscoelastic flow with an integral constitutive law, in the two spatial dimensions and in a periodic domain. Models that are included in these results are classical…

Analysis of PDEs · Mathematics 2013-12-02 Laurent Chupin

In this work, we study the global existence of strong solutions and large-time behavior of a two-phase fluid model in a bounded domain. The model consists of the isothermal Euler equations and the isentropic compressible Navier--Stokes…

Analysis of PDEs · Mathematics 2021-01-01 Jinwook Jung

This paper provides results on local and global existence for a class of solutions to the Euler equations for an incompressible, inviscid fluid. By considering a class of solutions which exhibits a characteristic growth at infinity we…

Analysis of PDEs · Mathematics 2009-02-27 Ralph Saxton , Feride Tiglay

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

This paper establishes the global well-posedness of solutions to the Oldroyd-B model with purely horizontal viscosity and arbitrarily large initial data in two-dimensional settings, including the full space $\mathbb{R}^2$, the partially…

Analysis of PDEs · Mathematics 2025-03-13 Zhenrong Nong , Yinghui Wang , Huancheng Yao , Shihao Zhang

The global existence of solutions to incompressible viscoelastic flows has been a longstanding open problem, even for the global weak solution. Under some special structure ("div-curl" condition) the global small smooth solution was…

Analysis of PDEs · Mathematics 2020-12-16 Yi Zhu

We investigate global strong solutions for the incompressible viscoelastic system of Oldroyd--B type with the initial data close to a stable equilibrium. We obtain the existence and uniqueness of the global solution in a functional setting…

Analysis of PDEs · Mathematics 2011-02-03 Ting Zhang , Daoyuan Fang

We prove the existence of global weak solutions with finite energy to some two-fluid systems with magnetic field and the results suit for corresponding two-fluid systems. The proof method is mainly inspired by Novotn\'y et al. and Vasseur…

Analysis of PDEs · Mathematics 2021-11-09 Lin Ma , Boling Guo , Jie Shao

We analyze a diffuse interface model for multi-phase flows of $N$ incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space…

Analysis of PDEs · Mathematics 2024-01-15 Helmut Abels , Harald Garcke , Andrea Poiatti

A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…

Analysis of PDEs · Mathematics 2017-04-06 Fucai Li , Yanmin Mu , Dehua Wang

We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes…

Analysis of PDEs · Mathematics 2020-07-22 Michal Bathory , Miroslav Bulíček , Josef Málek

The initial value problem for a coupled system is studied. The system consists of a differential inclusion and a differential equation and models the fluid flow of a viscoelastic fluid of Oldroyd type. The set-valued right-hand side of the…

Analysis of PDEs · Mathematics 2022-09-13 André Eikmeier

We study the equations of a two dimensional incompressible Newtonian fluid coupled with a dispersive parabolic-elliptic system on bounded domains. Global in time weak solutions are shown to exist and converge with a rate to the stationary…

Analysis of PDEs · Mathematics 2008-10-14 Rolf J. Ryham

We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space…

Analysis of PDEs · Mathematics 2017-05-15 Yoshikazu Giga , Slim Ibrahim , Shengyi Shen , Tsuyoshi Yoneda

The present paper deals with non Newtonian viscoelastic flows of Oldroyd-B tye in thin domains. Such geometries arise for example in the context of lubrication. More precisely, we justify rigorously the asymptotic model obtained…

Analysis of PDEs · Mathematics 2010-11-10 Guy Bayada , Laurent Chupin , Bérénice Grec

The global solutions in critical spaces to the multi-dimensional compressible viscoelastic flows are considered. The global existence of the Cauchy problem with initial data close to an equilibrium state is established in Besov spaces.…

Analysis of PDEs · Mathematics 2010-10-22 Xianpeng Hu , Dehua Wang

We prove conditions for global nonlinear stability of Oldroyd-B viscoelatic fluid flows in the Couette shear flow geometry. Global stability is inferred by analysing a new functional, called a perturbation entropy, to quantify the magnitude…

Fluid Dynamics · Physics 2023-08-14 Joshua Binns , Andrew Wynn

This paper studies the inviscid limit of the two-dimensional incompressible viscoelasticity, which is a system coupling a Navier-Stokes equation with a transport equation for the deformation tensor. The existence of global smooth solutions…

Analysis of PDEs · Mathematics 2019-07-11 Yuan Cai , Zhen Lei , Fanghua Lin , Nader Masmoudi