Mathematical Model of Dynamics of an Elastic Body in a Viscous Incompressible Fluid

In this paper, a mathematical model that describes the dynamics of an elastic body immersed in a viscous incompressible fluid is proposed. The displacement of the body is composed of a rigid motion (translation and rotation) combined with elastic deformations. Assuming the deformations to be small, we suppose that the form of the body does not change during the motion. At the same time, the velocity of the elastic deformations is not small and cannot be ignored. By this reason, at each point of the body, we put an oscillator that is described by the equations of linear elasticity. At the boundary of the body, the fluid velocity is matched with the sum of the velocities of the rigid motion and the elastic oscillations.