Electronic Research Archive

2021, Issue 6: 4269-4296. doi: 10.3934/era.2021085

Optimal control for the coupled chemotaxis-fluid models in two space dimensions

• Received: 01 August 2021 Revised: 01 September 2021 Published: 26 October 2021
• Primary: 92C17, 49J20; Secondary: 49K20, 35K51

• This paper deals with a distributed optimal control problem to the coupled chemotaxis-fluid models. We first explore the global-in-time existence and uniqueness of a strong solution. Then, we define the cost functional and establish the existence of Lagrange multipliers. Finally, we derive some extra regularity for the Lagrange multiplier.

Citation: Yunfei Yuan, Changchun Liu. Optimal control for the coupled chemotaxis-fluid models in two space dimensions[J]. Electronic Research Archive, 2021, 29(6): 4269-4296. doi: 10.3934/era.2021085

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• This paper deals with a distributed optimal control problem to the coupled chemotaxis-fluid models. We first explore the global-in-time existence and uniqueness of a strong solution. Then, we define the cost functional and establish the existence of Lagrange multipliers. Finally, we derive some extra regularity for the Lagrange multiplier.

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