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Existence and uniqueness of solution for fluid-plate interaction problem

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.