Nguyen Thanh Thuy, Vietnam National University, Ha Noi
Vu Duc Thi, Vietnam National University, Ha Noi
Le Hoai Bac, Vietnam National University, Ho Chi Minh
Tu Minh Phuong, Posts and Telecommunications Institute of Technology
Huynh Quyet Thang, Hanoi University of Science and Technology
Nguyen Huu Thanh, Hanoi University of Science and Technology
Luong Chi Mai, Vietnam Academy of Science and Technology
Tran Xuan Tu, Vietnam National University, Ha Noi
Truong Trung Kien, Posts and Telecommunications Institute of Technology
Tran Nguyen Ngoc, Le Quy Don Technical University
Hoang Van Phuc, Le Quy Don Technical University
Necessary optimality conditions for an optimal control problem of 2D gNavierStokes equations. 
Nguyen Duc Loc Keywords: gNavierStokes equations; existence of optimal solution; firstorder necessary optimality conditions. Abstract: Considered here is the optimal control problem of 2D gNavierStokes equations. We prove the existence of optimal solutions and establish the firstorder necessary optimality conditions. References [1] C.T. Anh and D.T. Quyet, "Longtime behavior for 2D nonautonomous gNavierStokes equations", Ann. Pol. Math. 103, pp 277302, 2012. [2] C.T. Anh, D.T. Quyet and D.T. Tinh, "Existence and finite time approximation of strong solutions of the 2D gNavierStokes equations", Acta. Math. Viet. 38, pp 417428, 2013. [3] D.T. Quyet, "Asymptotic behavior of strong solutions to 2D gNavierStokes equations", Comun. Korean Math. Soc. 29, pp 505518, 2014. [4] H. Bae and J. Roh, Existence of solutions of the gNavierStokes equations, Taiwanese J. Math. 8, pp 85102, 2004. [5] D.T. Quyet, "Pullback attractor for strong solutions of 2D nonautonomous gNavierStokes equations", Acta. Math.Viet. 40, pp 637651, 2015. [6] J. Roh, "Dynamics of the gNavierStokes equations", J. Differential Equations 211, pp 452484, 2005. [7] R. Temam, NavierStokes Equations: Theory and Numerical Analysis, 2nd edition, Amsterdam: NorthHolland, 1979. [8] R. Temam, NavierStokes Equations and Nonlinear functional Analysis, 2nd edition, Philadelphia, 1995. [9] F. Troltzsch and D. Wachsmuth, "Secondorder sufficient optimality conditions for the optimal control of NavierStokes equations", ESAIM Control Optim. Calc. Var. 12, pp 93119, 2006. [10] M. Ulbrich, "Constrained optimal control of NavierStokes flow by semismooth Newton methods", Systems and Control letters. 48, pp 297311, 2003. [11] D. Wachsmuth, "Optimal control of the unsteady NavierStokes equations", PhD thesis, TU Berlin, 2006. [12] D. Wachsmuth, "Regularity and stability of optimal controls of instationary NavierStokes equations", Control Cybernet. 34, pp 387410, 2005.
