Potential flow for the compressible viscous fluid and its incompressible limit

In this article we study and justify the incompressible limit of the potential flows of a compressible viscous fluid at small Reynolds number. We prove that the singular limit system for the potential flow of the viscous compressible fluid dynamics equations as the Mach number tends to zero is the Laplace equation combined with the linear part of the Bernoulli's equation. The strong compactness of the first corrector of the density, i.e., the acoustic wave is also obtained and is shown to satisfy the transport equation which describes the convection by incompressible velocity field of a scalar quantity.