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Well-posedness and optimal control for stochastic second grade fluids

GFM seminar
FCUL, C6, room 6.2.33
2016-06-29 14:30 .. 15:30
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by Fernanda Cipriano (Dep. de Matemática da Univ. Nova de Lisboa)

This work deals with stochastic second grade fluids, which are incompressible non-Newtonian type fluids. It is well known that small random perturbations of turbulent fluids can substantially modify their behavior; here the deterministic equations are perturbed by a multiplicative white noise. We study the existence and uniqueness of stochastic solutions on a two-dimensional bounded domain endowed with slip boundary conditions. We also address a control problem, where the control is effected through a distributed random force.

The well-posedness of the corresponding linearized equations is the main issue to analyze the Gâteau derivative of the control-to-state map.

The analysis of stochastic backward adjoint equations allows to establish the first order necessary optimality conditions.