论文标题
非自主随机纳维尔 - 斯托克斯方程的常规空间中随机吸引子的渐近自主性
Asymptotic Autonomy of Random Attractors in Regular Spaces for Non-autonomous Stochastic Navier-Stokes Equations
论文作者
论文摘要
本文涉及在有限的平滑域$ \ MATHCAL {O} $驱动的乘法和添加剂噪声驱动的非自主空间中的常规空间中的长期随机动力学。对于两种噪声驱动的方程式，我们演示了一种独特的回拔吸引子，它在$ \ mathbb {l}^2中是向后紧凑而渐近自主的，并且在$ \ mathbb {\ mathcal {o}）$和$ \ mathbb {h}该解决方案的向后均匀扁平特性用于证明常规空间$ \ mathbb {h} _0^1（\ Mathcal {O}）$ \ Mathbb {H} _0^1（\ Mathbb {o}）$的非自主随机动力学系统的向后均匀回调渐近渐近。
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 random dynamical systems in the regular space $\mathbb{H}_0^1(\mathcal{O})$.
