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In this paper, the authors study the asymptotic dynamical behavior for stochastic monopolar non-Newtonian fluids with multiplicative noise defined on a two-dimensional bounded domain, and prove the existence of an H-random attractor for the corresponding random dynamical system. A random attractor is a random compact set absorbing any bounded subset of the phase space V .

$H^1$-random attractors of stochastic monopolar non-Newtonian fluids with multiplicative noise