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Related papers: Large global solutions to the Oldroyd-B model with…

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We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like $\mu(\mathbf{D}) \sim |\mathbf{D}|^{p-2}$ ($p>\frac 65$) regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we…

Analysis of PDEs · Mathematics 2014-07-14 Ondřej Kreml , Milan Pokorný , Pavel Šalom

We consider the system of equations describing the flow of incompressible fluids in bounded domain. In the considered setting, the Cauchy stress tensor is a monotone mapping and has asymptotically $(s-1)$-growth with the parameter $s$…

Analysis of PDEs · Mathematics 2022-09-23 Miroslav Buliček , Piotr Gwiazda , Jakub Skrzeczkowski , Jakub Woźnicki

This paper is dedicated to the global well-posedness issue of the compressible Oldroyd-B model in the whole space $\R^d$ with $d\ge2$. It is shown that this set of equations admits a unique global solution in a certain critical Besov space…

Analysis of PDEs · Mathematics 2014-10-29 Ruizhao Zi

We derive a criterion for the breakdown of solutions to the Oldroyd-B model in $\R^3$ in the limit of zero Reynolds number (creeping flow). If the initial stress field is in the Sobolev space $H^m$, $m> 5/2$, then either a unique solution…

Analysis of PDEs · Mathematics 2007-09-11 Raz Kupferman , Claude Mangoubi , Edriss S. Titi

In this paper, we first prove the global existence of weak solutions to the d-dimensional incompressible inhomogeneous Navier-Stokes equations with initial data in critical Besov spaces, which satisfies a non-linear smallness condition. The…

Analysis of PDEs · Mathematics 2015-06-12 Jingchi Huang , Marius Paicu , Ping Zhang

By a new energy approach involved in the high frequencies and low frequencies decomposition in the Besov spaces, we obtain the optimal decay for the incompressible Oldroyd-B model without damping mechanism in $\mathbb{R}^n$ ($n\ge 2$). More…

Analysis of PDEs · Mathematics 2019-05-08 Xiaoping Zhai

We are concerned with the study of the Cauchy problem to the 3D compressible Hall-magnetohydrodynamic system. We first establish the unique global solvability of strong solutions to the system when the initial data are close to a stable…

Analysis of PDEs · Mathematics 2018-06-08 Fuyi Xu , Meiling Chi , Lishan Liu , Yonghong Wu

In this paper, we study the Cauchy problem of a two-phase flow system consisting of the compressible isothermal Euler equations and the incompressible Navier-Stokes equations coupled through the drag force, which can be formally derived…

Analysis of PDEs · Mathematics 2024-02-01 Feimin Huang , Houzhi Tang , Guochun Wu , Weiyuan Zou

We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…

Analysis of PDEs · Mathematics 2026-01-26 Anna Abbatiello , Miroslav Bulíček , Petr Kaplický

This work is concerned with the global existence of large solutions to the three-dimensional dissipative fluid-dynamical model, which is a strongly coupled nonlinear nonlocal system characterized by the incompressible…

Analysis of PDEs · Mathematics 2023-08-29 Jihong Zhao , Ying Li

We prove the existence of a unique large-data global-in-time weak solution to a class of models of the form $\mathbf{u}_{tt} = \mathrm{div}(\mathbb{T}) + \mathbf{f}$ for viscoelastic bodies exhibiting strain-limiting behaviour, where the…

Analysis of PDEs · Mathematics 2020-11-17 Miroslav Bulíček , Victoria Patel , Yasemin Şengül , Endre Süli

In this paper, we investigate a generic compressible two-fluid model with common pressure ($P^+=P^-$) in $\mathbb{R}^3$. Under some smallness assumptions, Evje-Wang-Wen [Arch Rational Mech Anal 221:1285--1316, 2016] obtained the global…

Analysis of PDEs · Mathematics 2022-04-25 Guochun Wu , Lei Yao , Yinghui Zhang

This paper is devoted to global existence and optimal decay rate of weak solutions to some inviscid Oldroyd-B models with center diffusion. By virtue of the properties of Calderon-Zygmund operator and the Littlewood-Paley decomposition…

Analysis of PDEs · Mathematics 2023-07-21 Wenjie Deng , Zhaonan Luo , Zhaoyang Yin

The two-dimensional (2D) incompressible Euler equations have been thoroughly investigated and the resolution of the global (in time) existence and uniqueness issue is currently in a satisfactory status. In contrast, the global regularity…

Analysis of PDEs · Mathematics 2013-08-09 Dhanapati Adhikari , Chongsheng Cao , Jiahong Wu , Xiaojing Xu

We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent…

Analysis of PDEs · Mathematics 2024-02-13 Xiang Bai , Changhui Tan , Liutang Xue

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

In this paper, we study the Cauchy problem for the linear and semilinear Moore-Gibson-Thompson (MGT) equation in the dissipative case. Concerning the linear MGT model, by utilizing WKB analysis associated with Fourier analysis, we derive…

Analysis of PDEs · Mathematics 2021-05-17 Wenhui Chen , Ryo Ikehata

We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in…

Analysis of PDEs · Mathematics 2016-04-19 Young-Pil Choi , Bongsuk Kwon

We consider a model for an incompressible visoelastic fluid. It consists of the Navier-Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature…

Analysis of PDEs · Mathematics 2019-10-23 Martin Kalousek

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