Maximal regularity for the Stokes system coupled with a wave equation: application to the system of interaction between a viscous incompressible fluid and an elastic wall

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. In order to show the existence of strong solutions for the corresponding coupled system, we study the linearized system coupling the Stokes system with a wave equation and we show that the corresponding semigroup is analytic. This result can be compared to the case where the elastic displacement is governed by a beam equation for which the corresponding semigroup is only of Gevrey class.

Automated summary

This paper investigates the interaction between a viscous incompressible fluid and an elastic structure. By studying the linearized system, the existence of strong solutions for the coupled system is shown, and the corresponding semigroup is proven to be analytic. This result is compared to the case where the elastic displacement is governed by a beam equation, which only yields a Gevrey class semigroup.