In this chapter, we present a different approach to the proof of existence of strong solutions to the compressible barotropic Navier-Stokes system on a moving domain. Although similar in nature, the results presented in this chapter are based on entirely different approach than in Chap. 6 . The main theorem of this chapter relies on application of the \(L^p - L^q\) maximal regularity parabolic estimates. There are few differences in the assumptions of the main theorem of this chapter with respect to the main theorem in Chap. 6 . For example, less regularity is required on the pressure, but its monotonicity has to be assumed. Most importantly, we deal only with the Dirichlet boundary condition. The reason is that the maximal regularity theory for the linearized compressible Navier-Stokes system, which is the crucial tool for our method, has not been developed for the Navier boundary condition yet. Moreover, we prove the existence of a global small solution to the studied problem together with appropriate decay estimates.