TY - JOUR
T1 - Optimal control for two-dimensional stochastic second grade fluids
AU - Chemetov, Nikolai
AU - Cipriano, Fernanda
N1 - info:eu-repo/grantAgreement/FCT/5876/147209/PT#
info:eu-repo/grantAgreement/FCT/5876/147204/PT#
Sem pdf conforme despacho.
PY - 2018/8
Y1 - 2018/8
N2 - 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.
AB - 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.
KW - Backward stochastic partial differential equations
KW - Necessary optimality condition
KW - Stochastic optimal control
KW - Stochastic second grade fluids
UR - http://www.scopus.com/inward/record.url?scp=85032219159&partnerID=8YFLogxK
U2 - 10.1016/j.spa.2017.09.016
DO - 10.1016/j.spa.2017.09.016
M3 - Article
AN - SCOPUS:85032219159
SN - 0304-4149
VL - 128
SP - 2710
EP - 2749
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 8
ER -