A study of stochastic viscoelastic fluid models and related constrained physical problems

Speaker: 

Debopriya Mukherjee

Affiliation: 

UNSW, Sydney.

Date: 

Tue, 22/05/2018 - 11:05am

Venue: 

RC-4082, The Red Centre, UNSW

Abstract: 

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.

 

 

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