On the Local Existence of Solutions to the compressible Navier–Stokes-Wave System with a Free Interface

Abstract

AbstractWe address a system of equations modeling a compressible fluid interacting with an elastic body in dimension three. We prove the local existence and uniqueness of a strong solution when the initial velocity belongs to the space $$H^{2+\epsilon }$$ H 2 + ϵ and the initial structure velocity is in $$H^{1.5+\epsilon }$$ H 1.5 + ϵ , where $$\epsilon \in (0,1/2)$$ ϵ ∈ ( 0 , 1 / 2 ) .