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Optimal Distributed Control of the Three-dimensional Planetary Geostrophic Equations

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Abstract

The main objective of this paper is to study the optimal distributed control of the three-dimensional planetary geostrophic equations. We apply the well-posedness and regularity results proved in Cao and Titi (Commun Pure Appl Math 56:198–233, 2003) to establish the existence of an optimal control as well as the first-order necessary optimality condition for an associated optimal control problem in which a distributed control is applied to the temperature.

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Acknowledgements

This work was supported by the National Science Foundation of China Grant (11401459, 11871389), the Natural Science Foundation of Shaanxi Province (2018JM1012) and the Fundamental Research Funds for the Central Universities (xjj2018088).

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  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Bo You

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  1. Bo You
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Correspondence to Bo You.

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You, B. Optimal Distributed Control of the Three-dimensional Planetary Geostrophic Equations. J Dyn Control Syst 28, 351–373 (2022). https://doi.org/10.1007/s10883-021-09570-1

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  • DOI: https://doi.org/10.1007/s10883-021-09570-1

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