Explanipedia

Preface Open

Desheng Li, Alain Miranville, Xin‐Guang Yang, Hongliang Zuo · 2025

On a fourth-order Allen-Cahn type equation with degenerate mobility Open

Wei Shi, Lu Li, Xin‐Guang Yang, Alain Miranville · 2025

International audience

Preface Open

Desheng Li, Alain Miranville, Xin‐Guang Yang, Hongliang Zuo · 2025

Asymptotic behavior of 3D Ladyzhenskaya-type fluid flow model with delay Open

Songmao He, Xin‐Guang Yang · 2024

This paper is concerned with the pullback dynamics and asymptotic stability of three dimensional Ladyzhenskaya-type incompressible fluid flow model with delay. Based on the existence and uniqueness of weak solutions, the tempered family of…

Robustness of Pullback Attractors for 2D Incompressible Navier-Stokes Equations with Delay Open

Keqin Su, Xin‐Guang Yang · 2024

This paper is concerned with the pullback dynamics and robustness for the 2D incompressible Navier-Stokes equations with delay on the convective term in bounded domain.Under appropriate assumption on the delay term, we establish the existe…

Gromov-Hausdorff stability of global attractors for the 3D incompressible Navier-Stokes-Voigt equations Open

Dongze Wang, Xin‐Guang Yang, Alain Miranville, Xingjie Yan · 2024

The structure stability from the Gromov-Hausdorff viewpoint can be used to describe the continuity of complete trajectories inside global attractors for nonlinear evolutionary partial differential equations defined on perturbed domains, su…

Dynamics of the three-dimensional Brinkman-Forchheimer-extended Darcy model in the whole space Open

Yan Lin, Chunxiao Guo, Xin‐Guang Yang, Alain Miranville · 2023

This paper is concerned with the pullback dynamics of a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model for porous media in the whole space. The existence and uniqueness of weak solutions is achieved firstly, leading …

Exponential stability of a transmission problem for wave equations with internal time‐varying delay and nonlinear degenerate weights Open

Meng Hu, Xin‐Guang Yang, Yanfang Li · 2023

This paper is concerned with a transmission problem for wave equations with internal time‐varying delay and nonlinear degenerate weights. Under some appropriate assumptions, the global well‐posedness and exponential stability are shown by …

Determination of Three-Dimensional Brinkman—Forchheimer-Extended Darcy Flow Open

Zhengwang Tao, Xin‐Guang Yang, Yan Lin, Chunxiao Guo · 2023

The aim of this study is to determine a 3D incompressible Brinkman–Forchheimer-extended Darcy fluid flow. Based on global well-posedness and regularity of solutions with a periodic boundary condition, the determining modes for weak and reg…

Asymptotic stability for 3D Brinkman-Forchheimer equation with delay on some unbounded domains Open

Rong Yang, Xuesi Kong, Xin‐Guang Yang · 2023

This paper is concerned with the long-time dynamics and asymptotic stability for the 3D Brinkman-Forchheimer equation with delay on some unbounded domains. The global well-posedness of the 3D Brinkman-Forchheimer flow is investigated by a …

Lamé system with weak damping and nonlinear time-varying delay Open

Xin‐Guang Yang, Shubin Wang, Marcio A. Jorge Silva · 2023

This article is concerned with the stability and dynamics for the weak damped Lamé system with nonlinear time-varying delay in a bounded domain. Under some appropriate assumptions, the global well-posedness and asymptotic stability are sho…

Asymptotic Stability for the 2D Navier–Stokes Equations with Multidelays on Lipschitz Domain Open

Ling-Rui Zhang, Xin‐Guang Yang, Keqin Su · 2022

This paper is concerned with the asymptotic stability derived for the two-dimensional incompressible Navier–Stokes equations with multidelays on Lipschitz domain, which models the control theory of 2D fluid flow. By a new retarded Gronwall…

Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry Open

Lan Huang, Zhiying Sun, Xin‐Guang Yang, Alain Miranville · 2022

This paper is concerned with the global solutions of the 3D compressible micropolar fluid model in the domain to a subset of bounded with two coaxial cylinders that present the solid thermo-insulated walls, which is in a thermodynamical s…

Determination of the 3D Navier-Stokes equations with damping Open

Wei Shi, Xin‐Guang Yang, Xingjie Yan · 2022

This paper is concerned the determination of trajectories for the three-dimensional Navier-Stokes equations with nonlinear damping subject to periodic boundary condition. By using the energy estimate of Galerkin approximated equation, the …

Dynamics for the 3D incompressible Navier-Stokes equations with double time delays and damping Open

Wei Shi, Xiaona Cui, Xuezhi Li, Xin‐Guang Yang · 2021

This paper is concerned with the tempered pullback attractors for 3D incompressible Navier-Stokes model with a double time-delays and a damping term. The delays are in the convective term and external force, which originate from the contro…

Asymptotic stability of 3D functional Brinkman-Forchheimer equation Open

Xin‐Guang Yang, Yong Yang, Wenjing Liu, Junzhao Zhang · 2021

This paper is concerned with the asymptotic stability of global weak and strong solutions for a 3D incompressible functional Brinkman-Forchheimer equation with delay. Under some appropriate assumptions on the external forces especially the…

An Erratum on "Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay" (Discrete Continuous Dynamic Systems, 40(3), 2020, 1493-1515) Open

Xin‐Guang Yang · 2021

This paper is an Erratum on "Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay" (Discrete Continuous Dynamic Systems, 40(3), 2020, 1493-1515).

Dynamics of a 3D Brinkman-Forchheimer equation with infinite delay Open

Wenjing Liu, Rong Yang, Xin‐Guang Yang · 2021

This paper is concerned with the pullback dynamics and asymptotic stability for a 3D Brinkman-Forchheimer equation with infinite delay. The well-posedness of weak solution to the 3D Brinkman-Forchheimer flow with infinite delay is investig…

Pullback dynamics of a 3D modified Navier-Stokes equations with double delays Open

Pan Zhang, Lan Huang, Rui Lu, Xin‐Guang Yang · 2021

This paper is concerned with the tempered pullback dynamics for a 3D modified Navier-Stokes equations with double time-delays, which includes delays on external force and convective terms respectively. Based on the property of monotone ope…

Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains Open

Xin‐Guang Yang, Rong-Nian Wang, Xingjie Yan, Alain Miranville · 2020

This paper is concerned with the tempered pullback dynamics of the 2D Navier-Stokes equations with sublinear time delay operators subject to non-homogeneous boundary conditions in Lipschitz-like domains. By virtue of the estimates of backg…

Stability and dynamics for a nonlinear one-dimensional full compressible non-Newtonian fluids Open

Xin Liu, Yongjin Lu, Xin‐Guang Yang · 2020

In this paper, we concern with the existence of global attractors for a one-dimensional full compressible non-Newtonian fluid model defined on bounded domain. Using some delicate regular estimates and energy functional to obtain the contin…

The fractal dimension of pullback attractors for the 2D Navier-Stokes equations with delay Open

Xin‐Guang Yang, Boling Guo, Chunxiao Guo, Desheng Li · 2020

This paper is concerned with the bounded fractal and Hausdorff dimension of the pullback attractors for 2D non-autonomous incompressible Navier-Stokes equations with constant delay terms. Using the construction of trace formula with two ba…

The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay Open

Xin‐Guang Yang, Lu Li, Xingjie Yan, Ling Ding · 2020

This paper concerns the stability of pullback attractors for 3D Brinkman-Forchheimer equation with delays. By some regular estimates and the variable index to deal with the delay term, we get the sufficient conditions for asymptotic stabil…

Longtime dynamics for a type of suspension bridge equation with past history and time delay Open

Gongwei Liu, Baowei Feng, Xin‐Guang Yang · 2020

In this paper, we investigate a suspension bridge equation with past history and time delay effects, defined in a bounded domain $ \Omega $ of $ \mathbb{R}^N $. Many researchers have considered the well-posedness, energy decay of solution …

Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry Open

Zhiying Sun, Lan Huang, Xin‐Guang Yang · 2020

This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a thermodyna…

Stability and dynamics of a weak viscoelastic system with memory and nonlinear time-varying delay Open

Xin‐Guang Yang, J. Zhang, Shu Wang · 2019

This paper is concerned with the stability and dynamics of a weak viscoelastic system with nonlinear time-varying delay. By imposing appropriate assumptions on the memory and sub-linear delay operator, we prove the global well-posedness an…

Uniform attractors for non-autonomous plate equations with -Laplacian perturbation and critical nonlinearities Open

Xin‐Guang Yang, Marcelo J. D. Nascimento, Maurício Luciano Pelicer · 2019

This paper is concerned with the long-time behavior for a class of non-autonomous plate equations with perturbation and strong damping of $ p $-Laplacian type \begin{document}$ u_{tt} + \Delta^2 u + a_{\epsilon}(t) u_t - \Delta_p u - \Delt…

Dynamics of 2D Navier-Stokes equations with Rayleigh's friction and distributed delay Open

Yadi Wang, Xin‐Guang Yang, Xingjie Yan · 2019

This article concerns the long time dynamics of a 2D incompressible Navier-Stokes equation with Rayleigh's friction and distributed delay. Under appropriate assumptions on the external force and delay term, we obtain global well-posedness …

Asymptotic behavior for 2D stochastic Navier-Stokes equations with memory in unbounded domains Open

Yadong Liu, Wenjun Liu, Xin‐Guang Yang · 2019

We consider a stochastic model which describes the motion of a 2D incompressible fluid in a unbounded domain with viscosity and memory effects. This model is different from the classical stochastic Navier-Stokes-Voigt equations due to the …

Pullback dynamics of 3D Navier–Stokes equations with nonlinear viscosity Open

Xin‐Guang Yang, Baowei Feng, Shubin Wang, Yongjin Lu, To Fu · 2019

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