An inviscid free boundary fluid-wave model

Abstract We consider the local existence and uniqueness of solutions for a system consisting an inviscid fluid with free boundary, modeled by Euler equations, in domain enclosed elastic which evolves according to wave equation. derive priori estimates also conclude uniqueness. Both, are obtained under assumption that data belongs $$H^{r}$$ H r , where $$r>2.5$$ > 2.5 is known be borderline exponent equations. Unlike setting equations vacuum, membrane shown stabilize sense Rayleigh–Taylor condition does not need assumed.