Shijie Shang
In this paper, we consider a stochastic model of incompressible second grade fluids on a bounded domain of R^2 driven by linear multiplicative Brownian noise with anticipating initial conditions. The existence and uniqueness of the solutions are established.
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In this paper, we establish the exponential mixing property of stochastic models for the incompressible second grade fluid. The general criterion established by Cyril Odasso plays an important role.
In this paper, we established a large deviation principle for stochastic models of incompressible second grade fluids. The weak convergence method introduced by \cite{Budhiraja-Dupuis} plays an important role.
In this paper, we establish a large deviation principle for stochastic models of two-dimensional second grade fluids driven by Lévy noise. The weak convergence method introduced by Budhiraja, Dupuis and Maroulas in [5] plays a key role.
We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ driven by Lévy noise. Applying the variational approach, global existence and uniqueness of strong probabilistic solution is established.
In this paper, we establish a moderate deviation principle for stochastic models of two-dimensional second grade fluids driven by Lévy noise. We will adopt the weak convergence approach. Because of the appearance of jumps, this result is significantly different from that in Gaussian case.
In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.
In this paper, we consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ with multiplicative noise. We first show that the solutions to the stochastic equations of second grade fluids generate a continuous random dynamical system. Second, we investigate the Fréchet differentiability of the random dynamical system. Finally, we establish the asymptotic compactness of the random dynamical system, and the existence of random attractors for the random dynamical system, we also obtain the upper semi-continuity of the perturbed random …
Inviscid Limit for Stochastic Second-Grade Fluid Equations
该研究针对带输运噪声的随机二阶流体方程，在光滑有界二维域中证明其解在合适初值正则性与参数条件下，可在L²范数时间一致意义下收敛到Euler方程解，无需边界层特定能量耗散，完善了无粘极限理论。
In this paper, we establish the well-posedness for the third grade fluid equation perturbed by a multiplicative white noise. This equation describes the motion of a non-Newtonian fluid of differential type with relevant viscoelastic properties. We are faced with a strongly nonlinear stochastic partial differential equation supplemented with a Navier slip boundary condition. Taking the initial condition in the Sobolev space H^2, we show the existence and the uniqueness of the strong (in the probability sense) solution in a two dimensional and non axisymmetric bounded domain.
Local strong solutions to the stochastic third grade fluid equations with Navier boundary conditions
本文研究二维和三维有界域上受非线性乘性Wiener噪声驱动的三阶非牛顿流体，结合截断逼近、随机紧性论证与Yamada-Watanabe定理，证明了取值于H^3的局部强路径解的存在唯一性。
On the Existence and long time behaviour of $H^{1}$-Weak Solutions for $2, 3d$-Stochastic $3^{rd}$-Grade Fluids Equations
本文研究了$d$维（$d=2,3$）有界单连通域上受乘性Wiener噪声扰动的不可压缩三阶流体方程，在Dirichlet边界条件和$H^1$初始数据下，结合随机紧性准则与单调性技巧证明了全局随机弱解的存在性，并分析了其长时间渐近行为。
Invariant measures for a class of stochastic third grade fluid equations in $2D$ and $3D$ bounded domains
本文研究了有界区域中乘性噪声下一类三阶流体方程的适定性与遍历不变测度，通过随机紧致性与单调性论证证明鞅解存在，利用稳定性获得强解，并基于 Feller 性质与 Krylov-Bogoliubov 定理证明了遍历不变测度的存在性。
Global-in-time optimal control of stochastic third-grade fluids with additive noise
本文研究了随机三级流体在加性噪声下的全局时间最优控制问题，通过将随机系统转化为确定性系统，证明了控制的最优性和解的存在性。
Large time behaviour for a class of 2D and 3D stochastic non-Newtonian fluids of differential types: Attractors and invariant measures
本文研究了随机三级流体方程在一般无界域上的大时间行为，证明了随机吸引子和不变测度的存在性，解决了随机吸引子、不变测度和遍历性方面的多个开放问题。
Optimal control of third grade fluids with multiplicative noise
本文研究受乘性 Wiener 噪声扰动的三级非牛顿流体的分布控制，通过停时代价、线性化、伴随方程与对偶关系证明最优控制存在并给出必要条件。
Large Deviations Principle for the Inviscid Limit of Fluid Dynamic Systems in 2D Bounded Domains
本文采用弱收敛方法，为受加性噪声扰动且粘性与噪声强度趋于零的二维有界域流体动力学系统建立大偏差原理，并在三种情形下证明了其在临界拓扑下的有效性。
Rate of convergence of random attractors towards deterministic singleton attractor for a class of non-Newtonian fluids of differential type
本文研究了非牛顿流体在随机扰动下吸引子收敛速度，证明了小扰动下吸引子退化为单点，并估计了噪声强度趋近于零时的收敛速度。
On Continuous Data Assimilation for a class of 2D and 3D stochastic non-Newtonian fluids of differential type
本文研究了针对一类随机非牛顿流体的连续数据同化方法，分析了观测网格大小和 nudging 收益的充分条件，证明了同化状态在均方意义下的收敛性，并在加性噪声情况下进一步证明了路径上的收敛性。
Random dynamics and invariant measures for a class of non-Newtonian fluids of differential type on 2D and 3D Poincaré domains
本文研究了二维和三维庞加莱域上一类非牛顿流体方程的随机动力学与不变测度，探讨了在不同边界条件下的解的适定性及随机吸引子的存在性。
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