The acoustic approximation for compressible flow in the presence of a surface undergoing small amplitude vibrations

Existence and uniqueness for short time is proved for the solutions of compressible isentropic flow in a bounded region with a moving boundary. These solutions have an asymptotic expansion in eta, the amplitude of the boundary motion, as eta approaches zero. The leading term in this expansion is a constant flow in a fixed region, and the second term is a solution of the linear acoustic equations in the fixed region which satisfies an inhomogeneous boundary condition.