A low Mach number limit of a dispersive Navier-Stokes system (Q2902739)

The authors consider the classical solutions to a compressible fluid system including the dispersive corrections to the Navier-Stokes equations in the whole space. The main result in this paper is to establish the low Mach number limit for such classical solutions, and show that the limiting equations is similar to a ghost effect system derived by \textit{Y. Sone} [Kinetic theory and fluid dynamics.. Modeling and Simulation in Science, Engineering and Technology. Basel: Birkhäuser (2002; Zbl 1021.76002)]. The analysis builds upon the framework developed by \textit{G. Métivier} and \textit{S. Schochet} [Arch. Ration. Mech. Anal. 158, No. 1, 61--90 (2001; Zbl 0974.76072)] and \textit{T. Alazard} [Arch. Ration. Mech. Anal. 180, No. 1, 1--73 (2006; Zbl 1108.76061)] for nondispersive systems. Their key arguments is to establish a priori estimates for the slow motion and fast motion. Then the desired convergence follow from the established local decay of the energy of the fast motion.