Local null controllability of a rigid body moving into a Boussinesq flow

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doi:10.3934/mcrf.2019050

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2019, Volume 9, Issue 4: 793-836. Doi: 10.3934/mcrf.2019050

This issue Previous Article Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions Next Article

Local null controllability of a rigid body moving into a Boussinesq flow

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1.
TIFR Centre for Applicable Mathematics, Post Bag No. 6503, GKVK Post Office, Bangalore 560065, India
2.
Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France

^* Corresponding author: Takéo Takahashi
^* Corresponding author: Takéo Takahashi

Received: December 31, 2017

Revised: August 31, 2019

Published: November 2019

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In this paper, we study the controllability of a fluid-structure interaction system. We consider a viscous and incompressible fluid modeled by the Boussinesq system and the structure is a rigid body with arbitrary shape which satisfies Newton's laws of motion. We assume that the motion of this system is bidimensional in space. We prove the local null controllability for the velocity and temperature of the fluid and for the position and velocity of rigid body for a control acting only on the temperature equation on a fixed subset of the fluid domain.

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Mathematics Subject Classification: Primary: 35Q30, 93C20; Secondary: 76D05, 93B05.

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