# Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations

Fredi Tröltzsch; Daniel Wachsmuth

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 1, page 93-119
- ISSN: 1292-8119

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topTröltzsch, Fredi, and Wachsmuth, Daniel. "Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations." ESAIM: Control, Optimisation and Calculus of Variations 12.1 (2006): 93-119. <http://eudml.org/doc/244824>.

@article{Tröltzsch2006,

abstract = {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^\infty $.},

author = {Tröltzsch, Fredi, Wachsmuth, Daniel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal control; Navier-Stokes equations; control constraints; second-order optimality conditions; first-order necessary conditions; second order optimality criterion},

language = {eng},

number = {1},

pages = {93-119},

publisher = {EDP-Sciences},

title = {Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations},

url = {http://eudml.org/doc/244824},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Tröltzsch, Fredi

AU - Wachsmuth, Daniel

TI - Second-order sufficient optimality conditions for the optimal control of Navier-Stokes equations

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2006

PB - EDP-Sciences

VL - 12

IS - 1

SP - 93

EP - 119

AB - 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^\infty $.

LA - eng

KW - optimal control; Navier-Stokes equations; control constraints; second-order optimality conditions; first-order necessary conditions; second order optimality criterion

UR - http://eudml.org/doc/244824

ER -

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