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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2019

Gevrey regularity for a system coupling the Navier-Stokes system with a beam equation

Résumé

We analyse a bi-dimensional fluid-structure interaction system composed by a viscous incompressible fluid and a beam located at the boundary of the fluid domain. Our main result is the existence and uniqueness of strong solutions for the corresponding coupled system. The proof is based on a the study of the linearized system and a fixed point procedure. In particular, we show that the linearized system can be written with a Gevrey class semigroup. The main novelty with respect to previous results is that we do not consider any approximation in the beam equation.
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Dates et versions

hal-02160011 , version 1 (19-06-2019)

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Mehdi Badra, Takéo Takahashi. Gevrey regularity for a system coupling the Navier-Stokes system with a beam equation. SIAM Journal on Mathematical Analysis, 2019, 51 (6), pp.4776-4814. ⟨10.1137/18M1196212⟩. ⟨hal-02160011⟩
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