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Second‐order sufficient optimality conditions for the optimal control of instationary Navier‐Stokes equations
Author(s) -
Tröltzsch Fredi,
Wachsmuth Daniel
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410295
Subject(s) - order (exchange) , subspace topology , function (biology) , mathematics , optimal control , navier–stokes equations , control (management) , mathematical optimization , control theory (sociology) , mathematical analysis , computer science , physics , compressibility , economics , artificial intelligence , finance , evolutionary biology , biology , thermodynamics
In this article sufficient optimality conditions are established for optimal control of evolutionary 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 ∞ . (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)