I will discuss about the existence of a solution to an optimal relaxed control problem for the linearly-coupled viscoelastic Oldroyd-B model driven by Levy noise. Then, the existence and uniqueness of local (maximal) strong solutions for the nonlinearly-coupled critical stochastic viscoelastic model in both two and three dimensions will be discussed. Furthermore, I will discuss about the weak (martingale) solutions to the nonlinearly-coupled critical and sub-critical stochastic Oldroyd-B model. In addition, I will prove the existence of an invariant measure for the sub-critical problem, using bw-Feller property of the associated Markov semigroup in a Poincare domain in two-dimensions.
Finally, I will move to the study on the effects of magnetization dynamics inside a ferromagnetic materials at low temperature taking values in a three-dimensional sphere in the form of the Landau-Lifshitz-Gilbert equations and prove the existence of a strong solution of the one-dimensional stochastic problem via Wong-Zakai approximation.