Applications of dispersive estimates to the acoustic pressure waves for incompressible fluid problems

The paper is devoted to the analysis of weak solutions of exterior problem for Navier-Stokes equations. It is stated that it is necessary to use a weak solution because the speed of acoustic waves in compressible models approximating Navier-Stokes equations tends to infinity. A definition of the weak solution is given. It is proved that a weak solution may be obtained as a limiting solution for a system with artificial compressibility and as a limiting solution for a Navier-Stokes-Poisson system. The first system is used for numerical calculations. The second system describes a real physical model. Some estimates for weak solutions are given.