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In the present work, we investigate stochastic third grade fluids equationsin a $d$-dimensional setting, for $d = 2, 3$. More precisely, on a bounded andsimply connected domain $\mathcal{D}$ of $\mathbb{R}^d$, $d = 2,3$, with asufficiently regular boundary $\partial \mathcal{D},$ we considerincompressible third grade fluid equations perturbed by a multiplicative Wienernoise. Supplementing our equations by Dirichlet boundary conditions and takinginitial data in the Sobolev space $H^1(\mathcal{D})$, we establish theexistence of global stochastic weak solutions by performing a strategy based onthe conjugation of stochastic compactness criteria and monotonicity techniques.Furthermore, we study the asymptotic behaviour of these solutions, as $t \to\infty$.

On the Existence and long time behaviour of $H^{1}$-Weak Solutions for $2, 3d$-Stochastic $3^{rd}$-Grade Fluids Equations