In this talk, we consider the random dynamics and asymptotic analysis of the well known mathematical model,
\\\\\\\\\\\\\\\\begin{align*}
\\\\\\\\\\\\\\\\frac{\\\\\\\\\\\\\\\\partial \\\\\\\\\\\\\\\\boldsymbol{v}}{\\\\\\\\\\\\\\\\partial t}-\\\\\\\\\\\\\\\\nu \\\\\\\\\\\\\\\\Delta\\\\\\\\\\\\\\\\boldsymbol{v}+(\\\\\\\\\\\\\\\\boldsymbol{v}\\\\\\\\\\\\\\\\cdot\\\\\\\\\\\\\\\\nabla)\\\\\\\\\\\\\\\\boldsymbol{v}+\\\\\\\\\\\\\\\\nabla p=\\\\\\\\\\\\\\\\boldsymbol{f}, \\\\\\\\\\\\\\\\ \\\\\\\\\\\\\\\\nabla\\\\\\\\\\\\\\\\cdot\\\\\\\\\\\\\\\\boldsymbol{v}=0,
\\\\\\\\\\\\\\\\end{align*}
the Navier-Stokes equations. We consider the two-dimensional stochastic Navier-Stokes equations (SNSE) driven by a \\\\\\\\\\\\\\\\textsl{linear multiplicative white noise of It\\\\\\\\\\\\\\\\^o type} on the whole space $\\\\\\\\\\\\\\\\mathbb{R}^2$. Firstly, we will discuss that the non-autonomous 2D SNSE generates a bi-spatial $(\\\\\\\\\\\\\\\\mathbb{L}^2(\\\\\\\\\\\\\\\\mathbb{R}^2),\\\\\\\\\\\\\\\\mathbb{H}^1(\\\\\\\\\\\\\\\\mathbb{R}^2))$-continuous random cocycle. Due to the bi-spatial continuity property of the random cocycle associated with SNSE, we will address that if the initial data is in $\\\\\\\\\\\\\\\\mathbb{L}^2(\\\\\\\\\\\\\\\\mathbb{R}^2)$, then there exists a unique bi-spatial $(\\\\\\\\\\\\\\\\mathbb{L}^2(\\\\\\\\\\\\\\\\mathbb{R}^2),\\\\\\\\\\\\\\\\mathbb{H}^1(\\\\\\\\\\\\\\\\mathbb{R}^2))$-pullback random attractor for non-autonomous SNSE which is compact and attracting not only in $\\\\\\\\\\\\\\\\mathbb{L}^2$-norm but also in $\\\\\\\\\\\\\\\\mathbb{H}^1$-norm. At the end, we will discuss the existence of an invariant measure for the random cocycle associated with 2D autonomous SNSE. We will also address the uniqueness of invariant measures for $\\\\\\\\\\\\\\\\boldsymbol{f}=\\\\\\\\\\\\\\\\mathbf{0}$ and for any $\\\\\\\\\\\\\\\\nu>0$ by using the linear multiplicative structure of the noise coefficient and exponential stability of solutions.