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Solutions to a fluid-structure interaction free boundary problem

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  • Our main result is the existence of solutions to the free boundary fluid-structure interaction system. The system consists of a Navier-Stokes equation and a wave equation defined in two different but adjacent domains. The interaction is captured by stress and velocity matching conditions on the free moving boundary lying in between the two domains. We prove the local existence of a solution when the initial velocity of the fluid belongs to $H^{3}$ while the velocity of the elastic body is in $H^{2}$.
    Mathematics Subject Classification: Primary: 35Q30, 74F10, 76D05; Secondary: 35K15, 35K55, 35M30.

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