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The Interaction of the 3D Navier-Stokes Equations with a Moving Nonlinear Koiter Elastic Shell

We study a moving boundary value problem consisting of a viscous incompressible fluid moving and interacting with a nonlinear elastic solid shell. The fluid motion is governed by the Navier–Stokes equations, while the shell is modeled by the nonlinear Koiter shell model, consisting of bending and membrane tractions as well as inertia. The fluid is coupled to the solid shell through continuity of displacements and tractions (stresses) along the moving material interface. We prove existence and uniqueness of solutions in Sobolev spaces.