Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Sharp decay rates of large solutions for the incompressible Phan-Thien–Tanner model in R3

Yuhui Chen, Minling Li and Zheng-an Yao
Applied Mathematics Letters 109996 (2026)
https://doi.org/10.1016/j.aml.2026.109996

Global well-posedness and incompressible limit of two-dimensional generalized compressible Oldroyd-B system with large velocity

Qibin Cheng, Yaobin Ou and Lu Yang
Discrete and Continuous Dynamical Systems - B (2026)
https://doi.org/10.3934/dcdsb.2026029

A linear HDG scheme for the diffusion type Peterlin viscoelastic problem

Sibang Gou, Jingyan Hu, Qi Wang, Feifei Jing and Guanyu Zhou
Journal of Computational and Applied Mathematics 475 117022 (2026)
https://doi.org/10.1016/j.cam.2025.117022

Global wellposedness and large time behavior of solutions to the incompressible polymeric flow

Tao Liang, Yuanyuan Dan and Xiaoping Zhai
Journal of Mathematical Physics 67 (1) (2026)
https://doi.org/10.1063/5.0290918

Optimal decay rate for the 2-D compressible Oldroyd-B and Hall-MHD models

Zhaonan Luo, Wei Luo and Zhaoyang Yin
Journal of Differential Equations 440 113443 (2025)
https://doi.org/10.1016/j.jde.2025.113443

Global regularity and sharp decay for incompressible Oldroyd-B model with only fractional dissipation of stress tensor

Weixun Feng, Dongdong Qin, Xianhua Tang and Rui Zhu
Bulletin of Mathematical Sciences 15 (02) (2025)
https://doi.org/10.1142/S166436072550002X

On the Cauchy Problem for a Simplified Compressible Oldroyd–B Model Without Stress Diffusion

Yuanyuan Dan, Feng Li, Haitao Ma and Yajuan Zhao
Mathematics 13 (16) 2589 (2025)
https://doi.org/10.3390/math13162589

A linear-decoupled and unconditionally energy stable fully discrete scheme for Peterlin viscoelastic model

Qi Wang, Kun Wang and Guanyu Zhou
Applied Numerical Mathematics 217 412 (2025)
https://doi.org/10.1016/j.apnum.2025.07.001

Global solutions to the three-dimensional inhomogeneous incompressible Phan-Thien–Tanner system with a class of large initial data

Yuhui Chen, Minling Li, Qinghe Yao and Zheng-an Yao
Nonlinearity 37 (9) 095035 (2024)
https://doi.org/10.1088/1361-6544/ad6b6f

Global Well-Posedness to the n-Dimensional Compressible Oldroyd-B Model Without Damping Mechanism

Xiaoping Zhai and Zhi-Min Chen
Journal of Dynamics and Differential Equations 36 (2) 1405 (2024)
https://doi.org/10.1007/s10884-023-10346-3

Global Well-Posedness and Optimal Time Decay Rates for the Compressible Oldroyd-B Model in $${\mathbb {R}}^2$$

Yuhui Chen, Minling Li, Qinghe Yao and Zheng-an Yao
Journal of Dynamics and Differential Equations 36 (4) 3311 (2024)
https://doi.org/10.1007/s10884-023-10292-0

Vanishing limit for the three-dimensional incompressible Phan-Thien–Tanner system

Yuhui Chen, Minling Li, Qinghe Yao and Zheng-an Yao
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 1 (2023)
https://doi.org/10.1017/prm.2023.27

Global existence and optimal time decay rates for the three-dimensional incompressible Phan-Thien–Tanner model

Yuhui Chen, Wei Luo and Zheng-an Yao
Analysis and Applications 21 (04) 931 (2023)
https://doi.org/10.1142/S0219530522500051

Global regularity for Oldroyd-B model with only stress tensor dissipation

Weixun Feng, Zhi Chen, Dongdong Qin and Xianhua Tang
Asymptotic Analysis 135 (3-4) 445 (2023)
https://doi.org/10.3233/ASY-231861

Global strong solutions and large time behavior to a micro-macro model for compressible polymeric fluids near equilibrium

Wenjie Deng, Wei Luo and Zhaoyang Yin
Journal of Differential Equations 370 378 (2023)
https://doi.org/10.1016/j.jde.2023.06.003

Sharp Rates of Decay and Global-in-Time Stability of Large Solutions to The Three-Dimensional Incompressible Phan-Thien–Tanner System of Polymeric Flows

Yuhui Chen, Minling Li, Qinghe Yao and Zheng-an Yao
SIAM Journal on Mathematical Analysis 55 (5) 4537 (2023)
https://doi.org/10.1137/21M1435161

Global Well-Posedness and Optimal Time Decay Rates for the Generalized Phan-Thien-Tanner Model in ℝ3

Yuhui Chen, Qinghe Yao, Minling Li and Zheng-an Yao
Acta Mathematica Scientia 43 (3) 1301 (2023)
https://doi.org/10.1007/s10473-023-0317-y

Global Regularity for the Incompressible Oldroyd-B Model with Only Stress Tensor Dissipation in Critical $${{\varvec{L}}}^{{{\varvec{p}}}}$$ Framework

Zhi Chen, Lvqiao Liu, Dongdong Qin and Weikui Ye
Journal of Mathematical Fluid Mechanics 24 (2) (2022)
https://doi.org/10.1007/s00021-022-00675-6

Global regularity for the generalized incompressible Oldroyd-B model with only stress tensor dissipation in critical Besov spaces

Jiahong Wu and Jiefeng Zhao
Journal of Differential Equations 316 641 (2022)
https://doi.org/10.1016/j.jde.2022.01.059

Global well-posedness and time decay for 2D Oldroyd-B-type fluids in periodic domains with dissipation in the velocity equation only

Hongxia Lin, Youhua Wei and Jiahong Wu
Nonlinear Analysis: Real World Applications 66 103513 (2022)
https://doi.org/10.1016/j.nonrwa.2022.103513

Global regularity for the 2D Oldroyd‐B model with fractional dissipation

Qianqian Xie and Zhuan Ye
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 102 (2) (2022)
https://doi.org/10.1002/zamm.202000363

The sharp time decay rates and stability of large solutions to the two-dimensional Phan-Thien–Tanner system with magnetic field

Yuhui Chen, Minling Li, Qinghe Yao and Zheng-an Yao
Asymptotic Analysis 129 (3-4) 451 (2022)
https://doi.org/10.3233/ASY-211736

Optimal time-decay rate of global classical solutions to the generalized compressible Oldroyd-B model

Shuai Liu and Yuzhu Wang
Evolution Equations and Control Theory 11 (4) 1201 (2022)
https://doi.org/10.3934/eect.2021041

Global existence in critical spaces for non Newtonian compressible viscoelastic flows

Xinghong Pan, Jiang Xu and Yi Zhu
Journal of Differential Equations 331 162 (2022)
https://doi.org/10.1016/j.jde.2022.05.020

Global well-posedness and inviscid limits of the generalized Oldroyd type models

Xiaoping Zhai, Yuanyuan Dan and Yongsheng Li
Nonlinear Analysis: Real World Applications 63 103414 (2022)
https://doi.org/10.1016/j.nonrwa.2021.103414

Sharp decay estimates for Oldroyd-B model with only fractional stress tensor diffusion

Peixin Wang, Jiahong Wu, Xiaojing Xu and Yueyuan Zhong
Journal of Functional Analysis 282 (4) 109332 (2022)
https://doi.org/10.1016/j.jfa.2021.109332

The sharp time decay rates for the incompressible Phan-Thien–Tanner system with magnetic field in R2

Yuhui Chen, Minling Li, Qinghe Yao and Zheng-an Yao
Applied Mathematics Letters 129 107965 (2022)
https://doi.org/10.1016/j.aml.2022.107965

Global existence and stability for the 2D Oldroyd-B model with mixed partial dissipation

Wen Feng, Weinan Wang and Jiahong Wu
Proceedings of the American Mathematical Society 150 (12) 5321 (2022)
https://doi.org/10.1090/proc/16039

The Global Existence and a Decay Estimate of Solutions to the Phan-Thein-Tanner Model

Ruiying Wei, Yin Li and Zheng-an Yao
Acta Mathematica Scientia 42 (3) 1058 (2022)
https://doi.org/10.1007/s10473-022-0314-6

Weak solutions of the three-dimensional hypoviscous elastodynamics with finite kinetic energy

Ke Chen and Jie Liu
Journal of Differential Equations 339 637 (2022)
https://doi.org/10.1016/j.jde.2022.08.031

Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem

Ramon Codina and Laura Moreno
ESAIM: Mathematical Modelling and Numerical Analysis 55 S279 (2021)
https://doi.org/10.1051/m2an/2020038

Global solutions to the n-dimensional incompressible Oldroyd-B model without damping mechanism

Xiaoping Zhai
Journal of Mathematical Physics 62 (2) (2021)
https://doi.org/10.1063/5.0010742

High Reynolds number and high Weissenberg number Oldroyd-B model with dissipation

Peter Constantin, Jiahong Wu, Jiefeng Zhao and Yi Zhu
Journal of Evolution Equations 21 (3) 2787 (2021)
https://doi.org/10.1007/s00028-020-00616-8

A mathematician’s perspective on the Oldroyd B model: Progress and future challenges

Michael Renardy and Becca Thomases
Journal of Non-Newtonian Fluid Mechanics 293 104573 (2021)
https://doi.org/10.1016/j.jnnfm.2021.104573

Global wellposedness and large time behavior of solutions to the N-dimensional compressible Oldroyd-B model

Xiaoping Zhai and Yongsheng Li
Journal of Differential Equations 290 116 (2021)
https://doi.org/10.1016/j.jde.2021.04.027

Global Well-Posedness and Decay Rates for the Three-Dimensional Compressible Phan-Thein–Tanner Model

Ruiying Wei, Yin Li and Zheng-an Yao
Journal of Mathematical Fluid Mechanics 23 (3) (2021)
https://doi.org/10.1007/s00021-021-00599-7

Global Well-posedness for the Three-Dimensional Generalized Phan–Thien–Tanner Model in Critical Besov Spaces

Yuhui Chen, Minling Li, Qinghe Yao and Zheng-an Yao
Journal of Mathematical Fluid Mechanics 23 (3) (2021)
https://doi.org/10.1007/s00021-021-00578-y

On the Cauchy Problem for a Compressible Oldroyd-B Model Without Stress Diffusion

Sili Liu, Yong Lu and Huanyao Wen
SIAM Journal on Mathematical Analysis 53 (6) 6216 (2021)
https://doi.org/10.1137/20M1362243

Weak solutions and invariant measures of stochastic Oldroyd-B type model driven by jump noise

Utpal Manna and Debopriya Mukherjee
Journal of Differential Equations 272 760 (2021)
https://doi.org/10.1016/j.jde.2020.10.009

Global Solutions to the 2-Dimensional Incompressible Oldroyd-B Model with Hybrid Dissipation and Partial Damping on Stress Tensor

Chao Deng, Qianjun He and Dunyan Yan
Results in Mathematics 76 (1) (2021)
https://doi.org/10.1007/s00025-020-01331-z

Global existence of classical solutions for the 3D generalized compressible Oldroyd‐B model

Yi Zhu
Mathematical Methods in the Applied Sciences 43 (10) 6517 (2020)
https://doi.org/10.1002/mma.6393

Regularity results for the 2D critical Oldroyd-B model in the corotational case

Zhuan Ye
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150 (4) 1871 (2020)
https://doi.org/10.1017/prm.2019.3

Global Well-Posedness in the Critical Besov Spaces for the Incompressible Oldroyd-B Model Without Damping Mechanism

Qionglei Chen and Xiaonan Hao
Journal of Mathematical Fluid Mechanics 21 (3) (2019)
https://doi.org/10.1007/s00021-019-0446-1

Optimal decay estimate of strong solutions for the 3D incompressible Oldroyd-B model without damping

Renhui Wan
Pacific Journal of Mathematics 301 (2) 667 (2019)
https://doi.org/10.2140/pjm.2019.301.667

Finite Amplitude Stability of Internal Steady Flows of the Giesekus Viscoelastic Rate-Type Fluid

Mark Dostalík, Vít Průša and Karel Tůma
Entropy 21 (12) 1219 (2019)
https://doi.org/10.3390/e21121219

Blow up and global existence for the periodic Phan-Thein-Tanner model

Yuhui Chen, Wei Luo and Zheng-an Yao
Journal of Differential Equations 267 (11) 6758 (2019)
https://doi.org/10.1016/j.jde.2019.07.005

An Osgood type regularity criterion for the 2D Oldroyd‐B model

Qionglei Chen and Xiaonan Hao
Mathematical Methods in the Applied Sciences 42 (5) 1652 (2019)
https://doi.org/10.1002/mma.5464

Global well-posedness for the Phan-Thein-Tanner model in critical Besov spaces without damping

Yuhui Chen, Wei Luo and Xiaoping Zhai
Journal of Mathematical Physics 60 (6) (2019)
https://doi.org/10.1063/1.5094086

On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium

S.V. Meleshko, N.P. Moshkin and V.V. Pukhnachev
International Journal of Non-Linear Mechanics 105 152 (2018)
https://doi.org/10.1016/j.ijnonlinmec.2018.06.002

Global Strong Solutions for Some Differential Viscoelastic Models

Laurent Chupin
SIAM Journal on Applied Mathematics 78 (6) 2919 (2018)
https://doi.org/10.1137/18M1186873

Relative Entropy, Weak-Strong Uniqueness, and Conditional Regularity for a Compressible Oldroyd--B Model

Yong Lu and Zhifei Zhang
SIAM Journal on Mathematical Analysis 50 (1) 557 (2018)
https://doi.org/10.1137/17M1128654

Mathematical study of a single leukocyte in microchannel flow

S. Boujena, O. Kafi, A. Sequeira, et al.
Mathematical Modelling of Natural Phenomena 13 (5) 43 (2018)
https://doi.org/10.1051/mmnp/2018045

Couette Flow of a Viscoelastic Maxwell-Type Medium with Two Relaxation Times

V. Yu. Liapidevskii
Proceedings of the Steklov Institute of Mathematics 300 (1) 137 (2018)
https://doi.org/10.1134/S008154381801011X

Global Existence Result for the Generalized Peterlin Viscoelastic Model

Mária Lukáčová-Medviďová, Hana Mizerová, Šárka Nečasová and Michael Renardy
SIAM Journal on Mathematical Analysis 49 (4) 2950 (2017)
https://doi.org/10.1137/16M1068505

Error analysis of finite element and finite volume methods for some viscoelastic fluids

Mária Lukáčová-Medvid’ová, Hana Mizerová, Bangwei She and Jan Stebel
Journal of Numerical Mathematics 24 (2) (2016)
https://doi.org/10.1515/jnma-2014-0057

Global regularity for the 2D Oldroyd‐B model in the corotational case

Zhuan Ye and Xiaojing Xu
Mathematical Methods in the Applied Sciences 39 (13) 3866 (2016)
https://doi.org/10.1002/mma.3834

Stationary Oldroyd model with diffusive stress: Mathematical analysis of the model and vanishing diffusion process

Laurent Chupin and Sébastien Martin
Journal of Non-Newtonian Fluid Mechanics 218 27 (2015)
https://doi.org/10.1016/j.jnnfm.2015.01.004

Global existence and uniqueness result for the diffusive Peterlin viscoelastic model

Mária Lukáčová - Medvid’ová, Hana Mizerová and Šárka Nečasová
Nonlinear Analysis: Theory, Methods & Applications 120 154 (2015)
https://doi.org/10.1016/j.na.2015.03.001

Unsteady rotational flows of an Oldroyd-B fluid due to tension on the boundary

A. Rauf, A.A. Zafar and I.A. Mirza
Alexandria Engineering Journal 54 (4) 973 (2015)
https://doi.org/10.1016/j.aej.2015.09.001

Global Existence Results for Some Viscoelastic Models with an Integral Constitutive Law

Laurent Chupin
SIAM Journal on Mathematical Analysis 46 (3) 1859 (2014)
https://doi.org/10.1137/130944746

Hyperbolic submodels of an incompressible viscoelastic Maxwell medium

V. Yu. Liapidevskii and V. V. Pukhnachev
Proceedings of the Steklov Institute of Mathematics 281 (1) 77 (2013)
https://doi.org/10.1134/S0081543813040081

MATHEMATICAL ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR AN AGING FLUID

DAVID BENOIT, LINGBING HE, CLAUDE LE BRIS and TONY LELIÈVRE
Mathematical Models and Methods in Applied Sciences 23 (09) 1561 (2013)
https://doi.org/10.1142/S0218202513500164

Global existence results for Oldroyd-B fluids in exterior domains

Matthias Hieber, Yuka Naito and Yoshihiro Shibata
Journal of Differential Equations 252 (3) 2617 (2012)
https://doi.org/10.1016/j.jde.2011.09.001

Global Well-Posedness for the 2D Micro-Macro Models in the Bounded Domain

Yongzhong Sun and Zhifei Zhang
Communications in Mathematical Physics 303 (2) 361 (2011)
https://doi.org/10.1007/s00220-010-1170-0

Initial value problems for creeping flow of Maxwell fluids

Toufik Laadj and Michael Renardy
Nonlinear Analysis: Theory, Methods & Applications 74 (11) 3614 (2011)
https://doi.org/10.1016/j.na.2011.03.010

Hall effects on hydromagnetic flow of an Oldroyd 6-constant fluid between concentric cylinders

M.A. Rana, A.M. Siddiqui and Rashid Qamar
Chaos, Solitons & Fractals 39 (1) 204 (2009)
https://doi.org/10.1016/j.chaos.2007.01.143

Multiscale Modeling and Simulation in Science

Claude Le Bris and Tony Lelièvre
Lecture Notes in Computational Science and Engineering, Multiscale Modeling and Simulation in Science 66 49 (2009)
https://doi.org/10.1007/978-3-540-88857-4_2

Global Well-Posedness for a Smoluchowski Equation Coupled with Navier-Stokes Equations in 2D

P. Constantin and Nader Masmoudi
Communications in Mathematical Physics 278 (1) 179 (2008)
https://doi.org/10.1007/s00220-007-0384-2

Well‐posedness for the FENE dumbbell model of polymeric flows

Nader Masmoudi
Communications on Pure and Applied Mathematics 61 (12) 1685 (2008)
https://doi.org/10.1002/cpa.20252

Global well-posedness of viscoelastic fluids of Oldroyd type in Besov spaces

Qionglei Chen and Changxing Miao
Nonlinear Analysis: Theory, Methods & Applications 68 (7) 1928 (2008)
https://doi.org/10.1016/j.na.2007.01.042

The effect of the slip condition on flows of an Oldroyd 6-constant fluid

T. Hayat, Masood Khan and M. Ayub
Journal of Computational and Applied Mathematics 202 (2) 402 (2007)
https://doi.org/10.1016/j.cam.2005.10.042