Workshop on Nonautonomous and Random Attractors
主办单位：华中科技大学数学与统计学院
(Sponsor: School of Mathematics and Statistics, HUST)
时间(Time)：2017.3.11-3.12
地点：华中科技大学数学与统计学院 科技楼 南楼 702室
(Address: No. 702, Keji Building, HUST)
Organizers
崔洪勇 (Hongyong Cui) (华中科技大学)
皮特. 科罗顿(Peter Kloeden) (华中科技大学)
杨美华(Meihua Yang) (华中科技大学)
Speakers
崔洪勇（Hongyong Cui） （华中科技大学）
高洪俊（Hongjun Gao） （南京师范大学）
韩晓莹（Xiaoying Han） （奥本大学，美国）
黄建华（Jianhua Huang） （国防科技大学）
蒋继发（Jifa Jiang） （上海师范大学）
皮特. 科罗顿(Peter Kloeden) （华中科技大学）
李扬荣（Yangrong Li） （西南大学）
刘国威（Guowei Liu） （上海交通大学）
卢松松 (Songsong Lu) (中山大学)
王业娟（Yejuan Wang） (兰州大学)
王兆娟（Zhaojuan Wang） (淮阴师范大学)
杨璐（Lu Yang） (兰州大学)
尤波（Bo You） (西安交通大学)
赵才地（Caidi Zhao ） (温州大学)
赵文强（Wenqiang Zhao） (重庆工商大学)
钟承奎 (Chengkui Zhong) (南京大学)
Schedule
日程表
2017年3月10日(星期五)：报到
2017.3.11，周六
时间发言人 主题
8:00 -- 8:10皮特. 科罗顿(Peter Kloeden)欢迎词
8:10 – 8:50蒋继发（Jifa Jiang）On Limiting Behavior of Stationary Measures for Stochastic Evolution Systems with Small Noise Intensity
8:50-- 9:30韩晓莹（Xiaoying Han）Attractors for non-autonomous lattice systems with switching effects and delayed recovery
9:30-10:10王业娟(Yejuan Wang)Multi-valued non-autonomous random dynamical systems
10:10-- 10:40 茶歇
10:40 -- 11:20黄建华(Jianhua Huang)Random attractors of non-Newtonian fluid flow driven by fractional Brownian Motion
11:20 – 11:50卢松松(Songsong Lu)Uniform global attractors for the nonautonomous 3D Navier–Stokes equations
12:00-13:00 绿园餐厅午餐
14:00 -- 14:40李扬荣(Yangrong Li)Random dynamics under unbounded perturbations of the domain
14:40—15:40皮特. 科罗顿(Peter Kloeden)Asymptotic invariance of forward attracting sets of nonautonomous dynamical systems
15:40 -- 16:10 茶歇
16:10-16:40王兆娟（Zhaojun Wang）Random Attractors for Non-Autonomous Stochastic Lattice FitzHugh-Nagumo Systems with Random Coupled Coecients
16:40 – 17:10赵文强(Wenqing Zhao)Regularity of random attractors for non-autonomous stochastic lattice dynamical systems in weighted spaces
17:10 – 17:40赵才地(Caidi Zhao)Pullback attractor and invariant measure for the globally modified Navier-Stokes equations
18:00 绿园餐厅晚餐
2017.3.12，周日
时间发言人主题
8:00 – 8:40钟承奎(Chengkui Zhong)Uniformly exponentially dissipative processes and exponential attraction
8:40 --9:20高洪俊(Hongjun Gao)Stochastic 3D Navier-Stokes equations with damping: well-posedness and dynamics
9:20 -- 9:50杨璐(Lu Yang)Dynamics for a stochastic reaction-diffusion equation with
dynamical boundary condition
9:50 – 10:20 茶歇
10:20 – 10:50刘国威(Guowei Liu)Pullback asymptotic behavior of solutions for a 2D non-autonomous non-Newtonian fluid
10:50 – 11:20尤波(Bo You)Finite dimensional global attractor of the Cahn-Hilliard-Navier-Stokes system with dynamic boundary condition
11:20 --11：50崔洪勇（Hongyong Cui）Uniform attractors for non-autonomous random dynamical systems
12:00 --13:00 绿园餐厅午餐
报告（一）
时间：2017年3月11日（星期六）8:10–8:50
报告人： 蒋继发
报告题目：On Limiting Behavior of Stationary Measures for
Stochastic Evolution Systems with Small Noise Intensity
报告摘要：The limiting behavior of stochastic evolution processes with small noise intensity ϵ is investigated in distribution-based approach. Let μ^ϵ be stationary measure for stochastic process X^ϵ with small ϵ and X^0 be a semiflow on a Polish space. Assume that {μ^ϵ : 0 <ϵ \leq ϵ_0} is tight. Then all their limits in weak sense are X^0-invariant and their supports are contained in Birkhoff center of X^0. Applications are made to various stochastic evolution systems, including stochastic ordinary differential equations, stochastic partial differential equations, stochastic functional differential equations driven by Brownian motion or Levy process.
This is a joint work with Dr. Chen Lifeng and Profs. Dong Zhao and Zhai Jianliang.
报告（二）
时间：2017年3月11日（星期六）8:50-9:30
报告人： 韩晓莹
报告题目：Attractors for non-autonomous lattice systems with switching effects and delayed recovery
报告摘要：The long term behavior of a type of non-autonomous lattice dynamical systems is investigated, where these have a diffusive nearest neighborhood interaction and discontinuous reaction terms with recoverable delays. This problem is of both biological and mathematical interests, due to its application in systems of excitable cells as well as general biological systems involving delayed recovery. The problem is formulated as an evolution inclusion with delays and the existence of weak and strong solutions is established. It is then shown that the solutions generate a set-valued non-autonomous dynamical system and that this non-autonomous dynamical system possesses a non-autonomous global pullback attractor.
报告（三）
时间：2017年3月11日（星期六）9:30-10:10
报告人： 王业娟
报告题目： Multi-valued non-autonomous random dynamical systems
报告摘要： We first present a sufficient and necessary condition for the existence of pullback attractors of multi-valued non-compact random dynamical systems. We then prove the existence of pullback attractors for reaction-diffusion equations with non-autonomous deterministic as well as stochastic forcing terms for which the uniqueness of solutions need not hold. In particular, the existence of pullback attractors in a space of higher regularity is established for the multi-valued non-compact random dynamical system associated with the reaction-diffusion equation with variable and infinite delays. Upper semicontinuity of pullback attractors for multi-valued non-compact random dynamical systems are also presented. Finally, the asymptotic behavior of stochastic systems with a Caputo fractional time derivative is investigated. In particular, the existence of a global forward attracting set in the mean-square topology is established.
报告（四）
时间：2017年3月11日（星期六）10:40-11:20
报告人： 黄建华
报告题目：Random attractors of non-Newtonian fluid flow driven by fractional
Brownian Motion
报告摘要：In this talks, we first present the regularity of stochastic convolution of fractional Brownian motion on the domain . Then, we present the global well-posedness and existence of random attractor of the stochastic non-Newtonian fluid and the stochastic modified Boussinesq approximate equations driven by fractional Brownian motion. Finally, we give an existence and uniqueness theory of pathwise mild solutions for a class of stochastic neutral partial functional differential equations that are driven by an infinite-dimensional multiplicative fractional Brownian motion.
报告（五）
时间：2017年3月11日（星期六）11:20-11:50
报告人： 卢松松
报告题目：Uniform global attractors for the nonautonomous
3D Navier–Stokes equations
报告摘要：We obtain the existence and the structure of the weak uniform (with respect to the initial time) global attractor and construct a trajectory attractor for the 3D Navier–Stokes equations (NSE) with a fixed time-dependent force satisfying a translation boundedness condition. Moreover, we show that if the force is normal and every complete bounded solution is strongly continuous, then the uniform global attractor is strong, strongly compact, and solutions converge strongly toward the trajectory attractor. Our method is based on taking a closure of the autonomous evolutionary system without uniqueness, whose trajectories are solutions to the nonautonomous 3D NSE. The established framework is general and can also be applied to other nonautonomous dissipative partial differential equations for which the uniqueness of solutions might not hold. It is not known whether previous frameworks can also be applied in such cases as we indicate in open problems related to the question of uniqueness of the Leray–Hopf weak solutions.
报告（六）
时间：2017年3月11日（星期六）14:00-14:40
报告人：李扬荣
报告题目：Random dynamics under unbounded perturbations of the domain
报告摘要：Under unbounded perturbations of the domain, expansion and restriction of a non-autonomous random dynamical system are investigated. Theoretical approximation results of bi-spatial random attractors are established when the domain becomes unbounded from bounded. Some criteria are obtained to ensure that the unbounded-domain attractor is approximated in both upper and lower semi-continuous sense, and also constructed by the metric-limit set of all bounded-domain attractors. These criteria are applied to prove that the stochastic FitzHugh-Nagumo coupled equations have an attractor in (H^1 \cap L^p) \times L^2 whether the domain is bounded or unbounded. Furthermore, we prove that the family of bounded-domain attractors is both upper and lower semi-continuous to the unbounded-domain attractor, which leads to a structure of the unbounded-domain attractor constructed by the metric-limit set of bounded-domain attractors. Under an additional tail-balance assumption, the unbounded-domain attractor can be constructed by the strong-limit set.
报告（七）
时间： 2017年3月11日（星期六）14:40-15:40
报告人：皮特. 科罗顿(Peter Kloeden)
报告题目：Asymptotic invariance of forward attracting sets of nonautonomous dynamical systems
报告摘要：The omega-limit set of a nonautonomous dynamical system is
shown to be asymptotic positive invariant in general and asymptotic negative invariant if the vector field is uniformly continuous in time. The upper semi-continuity of the omega limit sets in parameter follow from this result.
报告（八）
时间： 2017年3月11日（星期六）16:10-16:40
报告人： 王兆娟
报告题目：Random Attractors for Non-Autonomous Stochastic Lattice FitzHugh-Nagumo Systems with Random Coupled Coecients
报告摘要：We study the non-autonomous stochastic lattice FitzHugh-Nagumo system with random coupled coefficients and multiplicative white noise. We consider the existence of random attractors in a weighted space $ l_\rho ^2 \times l_\rho^2$ for this system, and establish the upper semicontinuity of random attractors as the intensity of noise approaches zero.
报告（九）
时间： 2017年3月11日（星期六）16:40-17:10
报告人： 赵文强
报告题目：Regularity of random attractors for non-autonomous stochastic lattice dynamical systems in weighted spaces
报告摘要：In this report, some sufficient conditions on the regularity of random attractors are first provided for general random dynamical systems in the weighted space $\ell_\rho^p\ (p>2)$ of infinite sequences. They are then used to study the asymptotic dynamics of a class of non-autonomous stochastic lattice differential equations with spatially valued additive noises.
报告（十）
时间： 2017年3月11日（星期六）17:10-17:40
报告人： 赵才地
报告题目： Pullback attractor and invariant measure for the globally modified Navier-Stokes equations
报告摘要：This talk studies the non-autonomous globally modified Navier-Stokes equations. We first prove that the associated process possesses a pullback attractor. Then we establish that there exists a unique family of Borel invariant probability measures on the pullback attractor.
报告（十一）
时间： 2017年3月12日（星期日）8:00-8:40
报告人： 钟承奎
报告题目: Uniformly exponentially dissipative processes and exponential attraction
报告摘要: We introduce a new concept of dissipativity called uniformly exponential dissipativity for processes, which provides a more general criterion for the exponential attraction of some non-autonomous dynamical systems. We apply it to some equations of mathematical physics including reaction-diffusion equations and damped wave equations in bounded domains.
报告（十二）
时间： 2017年3月11日（星期六）8:40-9:20
报告人： 高洪俊
报告题目： Stochastic 3D Navier-Stokes equations with damping: well-posedness and dynamics
报告摘要：In this talk, I will talk about the well-posedness, large deviation principle, ergodicity and attractor for stochaastic 3D Navier-Stokes equations with damping.
报告（十三）
时间： 2017年3月12日（星期日）9:20-9:50
报告人：杨璐
报告题目： Dynamics for a stochastic reaction-diffusion equation with dynamical boundary condition
报告摘要： In this talk, we study the dynamic behavior of a stochastic reaction-diffusion equation with dynamical boundary condition. Some higher-order integrability of the difference of the solutions near the initial time, and the continuous dependence result with respect to initial data were established. As a direct application, we can obtain the existence of pullback random attractor immediately.
报告（十四）
时间： 2016年4月17日（星期日）10:20-10:50
报告人： 刘国威
报告题目： Pullback asymptotic behavior of solutions for a 2D non-autonomous non-Newtonian fluid
报告摘要：This paper studies the pullback asymptotic behavior of solutions for a non-autonomous incompressible non-Newtonian fluid in 2D bounded domains. Firstly, with a little high regularity of the force, the semigroup method and $\epsilon$-regularity method are used to establish existence of compact pullback absorbing sets. Then, with a minimal regularity of the force, By verifying the flatting property also known as ``Condition (C)", they prove existence of pullback attractors for the universe of fixed bounded sets and for the another universe given by a tempered condition. Furthermore, they give the regularity of the pullback attractors.
报告（十五）
时间： 2017年3月12日（星期日）10:50-11:20
报告人： 尤波
报告题目： Finite dimensional global attractor of the Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions
报告摘要：In this talk, we are concerned with the existence of a finite dimensional global attractor of the Cahn-Hilliard-Navier-Stokes system with dynamic boundary conditions and a polynomial growth nonlinearity of arbitrary order. As we known, the existence of a global attractor in H \times V_I for the Cahn-Hilliard-Navier-Stokes system with dynamical boundary conditions can be proved by the Aubin-Lions compactness lemma, but the regularity of solutions obtained by making some energetic estimates and monotonicity arguments is not sufficient to prove the differentiability with respect to the initial values such that the standard scheme of estimating the fractal dimension of the global attractor does not work. To overcome this difficulty, we established the existence of a finite dimensional global attractor by the method of ℓ-trajectories
报告（十六）
时间： 2017年3月12日（星期日）11:20-11:50
报告人： 崔洪勇
报告题目: Uniform attractors for non-autonomous random dynamical systems
报告摘要：In this talk, we introduce a concept of random uniform attractor for non-autonomous RDS, as a generalization of Vishik's uniform attractor theory for deterministic non-autonomous dynamical systems. We first define the random uniform attractor as the minimal compact uniformly pullback attracting random set, and then establish several existence criteria and study further properties, including the forward uniformly attracting in probability, almost uniform attraction, etc. Remarkably, the relationship of random uniform attractors with usual random attractors and with multi-valued random attractors is given.
