On well-posedness and small data global existence for an interface damped free boundary fluid–structure model

We address a fluid?structure system which consists of the incompressible Navier?Stokes equations and a damped linear wave equation defined on two dynamic domains. The equations are coupled through transmission boundary conditions and additional boundary stabilization effects imposed on the free moving interface separating the two domains. Given sufficiently small initial data, we prove the global-in-time existence of solutions by establishing a key energy inequality which in addition provides exponential decay of solutions.

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