Recurrent Motions in the Nonautonomous Navier-Stokes System

Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation

We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equation $$u_t+Δ^2u+2Δu+au+b|\nabla u|^2+u^3=g(t,x).$$ We employ Conley index theory to show that, if the forcing $g:\mathbb{R}\rightarrow L^2(Ω)$ is a recurrent function, then there are at least two recurrent solutions in $H_0^2(Ω)$ under appropriate assumptions on the parameters $a$, $b$ and $g$.

非自治三维Navier-Stokes方程的一致全局吸引子

Uniform global attractors for the nonautonomous 3D Navier-Stokes equations

该研究针对含平移有界外力的非自治三维Navier-Stokes方程，通过构造无唯一性自治演化系统闭包的方法，得到弱一致全局吸引子的存在性与结构，建立了可推广至其他非自治耗散偏微分方程的通用框架。

具有循环非自治系数的强制性三次多项式常微分方程的全局分岔图

Global bifurcation diagrams for coercive third-degree polynomial ordinary differential equations with recurrent nonautonomous coefficients

本文研究具有循环非自治系数的强制性三次一阶标量 ODE，构造其全局分岔图，并用于解释带阈值迁移的 Allee 效应种群模型中的临界转变。

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

The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous dynamical systems. Second, they have obtained conditions of convergence of non-autonomous Navier-Stokes equations. Third, a criterion for the existence of almost periodic (quasi periodic,almost automorphic, recurrent, pseudo recurrent) solutions of non-autonomous Navier-Stokes equations is given. Finally, the authors have derived a global averaging principle f…

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。