Existence and uniqueness of solution for fluid-plate interaction problem

Abstract

In this paper, we study the interaction of an incompressible viscous fluid occupying two-dimensional channel with an elastic plate located on one part of fluid boundary. We assume that the deformation of the boundary is small enough and consider the fluid flow equations in the initial configuration. Non-steady Stokes equations are used to model the flow, and the pressure boundary conditions are prescribed on the channel’s ends. The results on existence, uniqueness, and regularity of solution are proved.

Keywords:

• fluid-structure interaction
• existence and uniqueness of the solution
• viscous fluid
• elastic plate

AMS Subject Classifications:

• 76D03
• 74F10
• 35Q30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the Ministry of Science, Education and Sports, Republic of Croatia [grant number 037-0372787-2797].