This chapter is devoted to the proof of existence of a strong solution to the compressible barotropic Navier-Stokes system on a moving domain on a short time interval provided the initial data are regular enough. The proof in this chapter is based on the application of energy methods, and we therefore work in the Hilbert spaces framework. The main theorem of this chapter is proved with the method of successive approximations. At each step, we solve a system consisting of linear continuity and momentum equations. The linear continuity equation is solved in a moving domain. This is possible since the characteristics are well defined due to the impermeability condition satisfied by the given velocity field. In order to solve the linear momentum equation, we use the Lagrangian transformation. This is allowed since the transformation depends only on the given vector field describing the motion of the domain, and therefore it is independent on the step of iteration. The main difficulty lies in appropriate estimates that give convergence of the iterative scheme. We restrict the presentation to the proof of the result for Navier slip boundary conditions. This case is more complicated as it requires treatment of the boundary terms which otherwise vanish.