Analyticity of the semigroup associated with a Stokes-wave interaction system and application to the system of interaction between a viscous incompressible fluid and an elastic structure - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Journal of Evolution Equations Year : 2022

Analyticity of the semigroup associated with a Stokes-wave interaction system and application to the system of interaction between a viscous incompressible fluid and an elastic structure

Abstract

We consider a viscous incompressible fluid interacting with an elastic structure located on a part of its boundary. The fluid motion is modeled by the bi-dimensional Navier-Stokes system and the structure follows the linear wave equation in dimension 1 in space. Our aim is to study the linearized system coupling the Stokes system with a wave equation and to show that the corresponding semigroup is analytic. In particular the linear system satisfies a maximal regularity property that allows us to deduce the existence and uniqueness of strong solutions for the nonlinear system. This result can be compared to the case where the elastic structure is a beam equation for which the corresponding semigroup is only of Gevrey class.
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Dates and versions

hal-03323092 , version 1 (20-08-2021)

Identifiers

  • HAL Id : hal-03323092 , version 1

Cite

Mehdi Badra, Takéo Takahashi. Analyticity of the semigroup associated with a Stokes-wave interaction system and application to the system of interaction between a viscous incompressible fluid and an elastic structure. Journal of Evolution Equations, 2022. ⟨hal-03323092⟩
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