Almost Periodic Solutions and Global Attractors of Non-autonomous Navier-Stokes Equations

Lagrangian structures for the Stokes, Navier-Stokes and Euler equations

We prove that the Navier-Stokes, the Euler and the Stokes equations admit a Lagrangian structure using the stochastic embedding of Lagrangian systems. These equations coincide with extremals of an explicit stochastic Lagrangian functional, i.e. they are stochastic Lagrangian systems in the sense of [Cresson-Darses, J. Math. Phys. 48, 072703 (2007]

Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions

We consider two-dimensional nonstationary Navier-Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain. We prove the existence of global in time solutions of the considered problem which is governed by a partial differential inclusion with a multivalued term in the form of Clarke subdifferential. Then we prove the existence of a trajectory attractor and a weak global attractor for the associated multivalued semiflow. This research is motivated by control problems for fluid flows in domains with semipermeable walls and membranes.

具有非线性色噪声的三维随机Navier-Stokes方程的全局随机吸引子

Global random attractor for 3D stochastic Navier-Stokes equation with nonlinear colored noise

本文引入与随机演化半群相关的随机演化系统及其全局弱/强随机吸引子的定义，建立存在性、不变性和跟踪性质，并应用于三维随机Navier-Stokes方程。

Longtime behavior for 3D Navier-Stokes equations with constant delays

This paper investigates the longtime behavior of delayed 3D Navier-Stokes equations in terms of attractors. The study will strongly rely on the investigation of the linearized Navier-Stokes system, and the relationship between the discrete dynamical flow for the linearized system and the continuous flow associated to the original system. Assuming the viscosity to be sufficiently large, there exists a unique local attractor for the delayed 3D Navier-Stokes equations. Moreover, the local attractor reduces to a singleton set.

带乘性白噪声的随机 Nernst-Planck-Navier-Stokes 系统的随机吸引子

Random attractors for the stochastic Nernst-Planck-Navier-Stokes system with multiplicative white noise

针对受乘性白噪声扰动的二维周期随机 Nernst-Planck-Navier-Stokes 方程，论文通过确定性变换证明全局适定性、构造随机动力系统，并证明紧随机吸引子的存在性及其噪声趋于零时的上半连续性。

Asymptotic Autonomy of Random Attractors in Regular Spaces for Non-autonomous Stochastic Navier-Stokes Equations

This article concerns the long-term random dynamics in regular spaces for a non-autonomous Navier-Stokes equation defined on a bounded smooth domain $\mathcal{O}$ driven by multiplicative and additive noise. For the two kinds of noise driven equations, we demonstrate the existence of a unique pullback attractor which is backward compact and asymptotically autonomous in $\mathbb{L}^2(\mathcal{O})$ and $\mathbb{H}_0^1(\mathcal{O})$, respectively. The backward-uniform flattening property of the solution is used to prove the backward-uniform pullback asymptotic compactness of the non-autonomous ra…

分布依赖的2D随机Navier-Stokes方程在非线性噪声驱动下的均匀测度吸引子

Uniform measure attractors of the distribution-dependent 2D stochastic Navier-Stokes equations driven by nonlinear noise

本文研究了由非线性噪声驱动且受近周期性外部强迫作用的分布依赖非自治2D随机Navier-Stokes方程的均匀测度吸引子。通过提出关于时间依赖外部强迫和分布依赖非线性项的充分条件，建立了系统解的唯一性和存在性。

McKean--Vlasov随机Navier--Stokes方程的弱平均原理与弱拉回吸引子

Weak Averaging Principle and Weak Pullback Attractors for Mckean--Vlasov Stochastic Navier--Stokes Equations

本文针对环面上带快速振荡系数的分布依赖随机Navier--Stokes方程，建立了三个弱平均原理，证明了弱拉回吸引子上半连续收敛到平均方程的弱全局吸引子。

The Convolution Series Solution of Divergent Navier-Stokes Equations

This paper gives out the solution of divergent Navier-Stokes equations, and shows that in this case, under a physicalacceptable condition, the solution would be smooth .