$L^p$ theory for the interaction between the incompressible Navier-Stokes system and a damped plate - Inria - Institut national de recherche en sciences et technologies du numérique
Journal Articles Journal of Mathematical Fluid Mechanics Year : 2021

$L^p$ theory for the interaction between the incompressible Navier-Stokes system and a damped plate

Abstract

We consider a viscous incompressible fluid governed by the Navier-Stokes system written in a domain where a part of the boundary is moving as a damped beam under the action of the fluid. We prove the existence and uniqueness of global strong solutions for the corresponding fluid-structure interaction system in an Lp-Lq setting. The main point in the proof consists in the study of a linear parabolic system coupling the non stationary Stokes system and a damped beam. We show that this linear system possesses the maximal regularity property by proving the R-sectoriality of the corresponding operator. The proof of the main results is then obtained by an appropriate change of variables to handle the free boundary and a fixed point argument to treat the nonlinearities of this system.
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Dates and versions

hal-02294097 , version 1 (23-09-2019)
hal-02294097 , version 2 (22-05-2020)

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Cite

Debayan Maity, Takéo Takahashi. $L^p$ theory for the interaction between the incompressible Navier-Stokes system and a damped plate. Journal of Mathematical Fluid Mechanics, 2021, ⟨10.1007/s00021-021-00628-5⟩. ⟨hal-02294097v2⟩
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