Local null controllability of a two-dimensional
fluid-structure interaction problemhttps://hal.inria.fr/inria-00542535/documentLaboratoire Jacques-Louis Lions (LJLL) ; INRIA - Université Paris VII -
Paris Diderot - Université Pierre et Marie Curie (UPMC) - Paris VI -
CNRSDepartamento de Ingeniería Mecánica (DIMEC) ; Universidad de
ChileHAL CCSDIn this paper, we prove a controllability result for a fluid-structure
interaction problem. In dimension two, a rigid structure moves into an
incompressible fluid governed by Navier-Stokes equations. The control acts on a
fixed subset of the fluid domain. We prove that, for small initial data, this
system is null controllable, that is, for a given T > 0, the system can be
driven at rest and the structure to its reference configuration at time T. To
show this result, we first consider a linearized system. Thanks to an
observability inequality obtained from a Carleman inequality, we prove an
optimal controllability result with a regular control. Next, with the help of
Kakutani's fixed point theorem and a regularity result, we pass to the nonlinear
problem.Boulakia, MurielOsses, Axel[MATH:MATH_AP] Mathematics/Analysis
of PDEs[MATH:MATH_AP]
Mathématiques/Equations aux dérivées partiellesPhysics::Fluid Dynamics[MATH.MATH-AP] Mathematics/Analysis
of PDEs2007-01-01oai:hal.inria.fr:inria-00542535oai:HAL:inria-00542535v1truefalse0.9dedup-similarity-resultconicytf____::6077d5a9d08dfb420cc7a1528939b09fhttp://repositorio.conicyt.cl/handle/10533/162859CONTROLABILIDAD DE EDP'S, CONTINUACION UNICA, DESIGUALDADES DE CARLEMAN Y
APLICACIONES. CONTROLLABILITY OF PDE'S, UNIQUE CONTINUATION, CARLEMAN
INEQUALITIES AND APPLICATIONS.conicytf____::CONICYT::FONDECYTconicytf____::CONICYT::FONDECYT::REGULAR1030808Local null controllability of a two-dimensional
fluid-structure interaction problemHAL CCSD2007-01-01Local null controllability of a two-dimensional
fluid-structure interaction problem2007-01-012007-01-01https://hal.inria.fr/inria-00542535/documenthttps://hal.inria.fr/inria-005425352007-01-01http://hal.inria.fr/docs/00/54/25/35/PDF/paperBO.pdfhttp://hal.inria.fr/inria-00542535e−2sV µ s1ϕ ¡|Δv|2 + |∂tv|2¢ + sλ2ϕ|∇v|2 + s3λ4ϕ3|v|2 2 2 Z τ λ[1] S. Anita, V. Barbu, Null controllability of nonlinear convective heat
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