Pontryagin's principle for local solutions of optimal control governed by the 2D Navier-Stokes equations with mixed control-state constraints

Huaiqiang Yu; Bin Liu

doi:10.3934/mcrf.2012.2.61

Article Contents

2012, Volume 2, Issue 1: 61-80. Doi: 10.3934/mcrf.2012.2.61

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Pontryagin's principle for local solutions of optimal control governed by the 2D Navier-Stokes equations with mixed control-state constraints

Huaiqiang Yu^1, and
Bin Liu^1,

1.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei

Received: May 31, 2011

Revised: October 31, 2011

Published: February 2012

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Abstract

This paper deals with the Pontryagin's principle of optimal control problems governed by the 2D Navier-Stokes equations with integral state constraints and coupled integral control--state constraints. As an application, the necessary conditions for the local solution in the sense of $L^r(0,T;L^2(\Omega))$ ($2 < r < \infty$) are also obtained.

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Mathematics Subject Classification: Primary: 35Q30, 49K20; Secondary: 93C20.

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