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

Fredi Tröltzsch; Daniel Wachsmuth

ESAIM: Control, Optimisation and Calculus of Variations (2005)

- 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 (2005): 93-119. <http://eudml.org/doc/90792>.

@article{Tröltzsch2005,

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 Ls-neighborhood,
whereby the underlying analysis allows to use weaker norms than L∞.
},

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.; optimal control; second order optimality criterion},

language = {eng},

month = {12},

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/90792},

volume = {12},

year = {2005},

}

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

DA - 2005/12//

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 Ls-neighborhood,
whereby the underlying analysis allows to use weaker norms than L∞.

LA - eng

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

UR - http://eudml.org/doc/90792

ER -

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