Well-posedness for the compressible Navier–Stokes–Lamé system with a free interface

We address the system of fluid–structure interaction consisting of a compressible Navier–Stokes equation coupled with an elasticity equation, with the velocity and stress continuity requirements across the free moving interface. We prove the a priori estimates for existence of solutions when the initial velocity belongs to H 3 , the initial density is bounded from below and belongs to H 3/2+r , where r> 0, and the initial velocity of the displacement is in H 3/2+r .

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