Periodic attractors of random truncator maps

Periodic and Almost Periodic Random Inertial Manifolds for Non-Autonomous Stochastic Equations

By the Lyapunov-Perron method,we prove the existence of random inertial manifolds for a class of equations driven simultaneously by non-autonomous deterministic and stochastic forcing. These invariant manifolds contain tempered pullback random attractors if such attractors exist. We also prove pathwise periodicity and almost periodicity of inertial manifolds when non-autonomous deterministic forcing is periodic and almost periodic in time, respectively.

无界区域上McKean-Vlasov随机反应扩散方程的不变测度、周期测度与拉回测度吸引子

Invariant measures, periodic measures and pullback measure attractors of McKean-Vlasov stochastic reaction-diffusion equations on unbounded domains

本文研究了R^n上非自治McKean-Vlasov随机反应扩散方程的长期动力学，证明了拉回测度吸引子、不变测度与周期测度的存在唯一性，并建立了系统收敛时的上半连续性与测度收敛性。

Existence, Stability and Bifurcation of Random Complete and Periodic Solutions of Stochastic Parabolic Equations

In this paper, we study the existence, stability and bifurcation of random complete and periodic solutions for stochastic parabolic equations with multiplicative noise. We first prove the existence and uniqueness of tempered random attractors for the stochastic equations and characterize the structures of the attractors by random complete solutions. We then examine the existence and stability of random complete quasi-solutions and establish the relations of these solutions and the structures of tempered attractors. When the stochastic equations are incorporated with periodic forcing, we obtain…

Large time behavior of the deterministic and stochastic 3D convective Brinkman-Forchheimer equations in periodic domains

The large time behavior of the deterministic and stochastic three dimensional convective Brinkman-Forchheimer (CBF) equations for $r\geq3$ ($r>3$, for any $μ$ and $β$, and $r=3$ for $2βμ\geq1$), in periodic domains is carried out in this work. Our first goal is to prove the existence of global attractors for the 3D deterministic CBF equations. Then, we show the existence of random attractors for the 3D stochastic CBF equations perturbed by small additive smooth noise. Finally, we establish the upper semicontinuity of random attractor for the 3D stochastic CBF equations (stability of attractors…

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。

Random attractor of the 3D viscous primitive equations driven by fractional noises

We develop a new and general method to prove the the existence of the random attractor (strong attractor) for the primitive equations (PEs) of large-scale ocean and atmosphere dynamics under $non$-$periodic$ boundary conditions and driven by infinite-dimensional additive fractional Wiener processes. In contrast to our new method, the common method, compact Sobolev embedding theorem, is to obtain the uniform $a$ $priori$ estimates in some Sobolev space whose regularity is high enough. But this is very complicated for the 3D stochastic PEs with the $non$-$periodic$ boundary conditions. Therefore…