Optimal control for two-dimensional stochastic second grade fluids

Nikolai Chemetov, Fernanda Cipriano

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


This article deals with a stochastic control problem for certain fluids of non-Newtonian type. More precisely, the state equation is given by the two-dimensional stochastic second grade fluids perturbed by a multiplicative white noise. The control acts through an external stochastic force and we search for a control that minimizes a cost functional. We show that the Gâteaux derivative of the control to state map is a stochastic process being the unique solution of the stochastic linearized state equation. The well-posedness of the corresponding stochastic backward adjoint equation is also established, allowing to derive the first order optimality condition.

Original languageEnglish
Pages (from-to)2710-2749
JournalStochastic Processes and their Applications
Issue number8
Publication statusPublished - Aug 2018


  • Backward stochastic partial differential equations
  • Necessary optimality condition
  • Stochastic optimal control
  • Stochastic second grade fluids


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