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Turnpike Property for Two-Dimensional Navier–Stokes Equations

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Abstract

In this paper we study the turnpike phenomenon arising in the optimal distributed control tracking-type problem for the Navier–Stokes equations. We obtain a positive answer to this property in the case when the control is time-dependent function and also when it is independent of time. In both cases we prove an exponential turnpike property assuming that the stationary optimal state satisfies certain properties of smallness.

Keywords

Navier–Stokes equations Optimal control problems Turnpike property Asymptotic stability Oseen equation 

Mathematics Subject Classification

Primary 35Q30 Secondary 49J20 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática y Ciencia de la ComputaciónUniversidad de Santiago de ChileSantiagoChile

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