Geodesic
Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 93-119

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In this paper sufficient optimality conditions are established for optimal control of both steady-state and instationary Navier-Stokes equations. The second-order condition requires coercivity of the Lagrange function on a suitable subspace together with first-order necessary conditions. It ensures local optimality of a reference function in a L s -neighborhood, whereby the underlying analysis allows to use weaker norms than L ∞ .

DOI : 10.1051/cocv:2005029
Classification : 49K20, 49K27
Keywords: optimal control, Navier-Stokes equations, control constraints, second-order optimality conditions, first-order necessary conditions 
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     author = {Tr\"oltzsch, Fredi and Wachsmuth, Daniel},
     title = {Second-order sufficient optimality conditions for the optimal control of {Navier-Stokes} equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {93--119},
     publisher = {EDP-Sciences},
     volume = {12},
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     year = {2006},
     doi = {10.1051/cocv:2005029},
     mrnumber = {2192070},
     zbl = {1111.49017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005029/}
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Tröltzsch, Fredi; Wachsmuth, Daniel. Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 1, pp. 93-119. doi: 10.1051/cocv:2005029

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