Remote trajectory tracking of a rigid body in an incompressible fluid at low Reynolds number

Kolumbán, József J.

doi:10.5802/crmath.374

Équations aux dérivées partielles, Théorie du contrôle

Remote trajectory tracking of a rigid body in an incompressible fluid at low Reynolds number

Kolumbán, József J.¹

¹ Budapest University of Technology and Economics, Department of Differential Equations, 1111 Budapest, Egry József u. 1 Building H, room H42

Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1135-1144.

Résumé

In this paper we study the motion of a rigid body driven by Newton’s law immersed in a stationary incompressible Stokes flow occupying a bounded simply connected domain. The aim is that of trajectory tracking of the solid by the means of a control in the form of Dirichlet boundary data on the outside boundary of the fluid domain. We show that it is possible to exactly achieve any smooth trajectory for the solid that stays away from the external boundary, by the means of such a remote control. The proof relies on some density methods for the Stokes system, as well as a reformulation of the solid equations into an ODE.

Reçu le : 2022-02-28
Révisé le : 2022-05-06
Accepté le : 2022-05-06
Publié le : 2022-10-04

DOI : 10.5802/crmath.374

Affiliations des auteurs :

Kolumbán, József J. ¹

¹ Budapest University of Technology and Economics, Department of Differential Equations, 1111 Budapest, Egry József u. 1 Building H, room H42

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     author = {Kolumb\'an, J\'ozsef J.},
     title = {Remote trajectory tracking of a rigid body in an incompressible fluid at low {Reynolds} number},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1135--1144},
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Kolumbán, József J. Remote trajectory tracking of a rigid body in an incompressible fluid at low Reynolds number. Comptes Rendus. Mathématique, Tome 360 (2022) no. G10, pp. 1135-1144. doi : 10.5802/crmath.374. http://www.numdam.org/articles/10.5802/crmath.374/

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