A Low Mach Number Limit of a Dispersive Navier–Stokes System

We establish a low Mach number limit for classical solutions over the whole space of a compressible fluid dynamic system that includes dispersive corrections to the Navier-Stokes equations. The limiting system is similar to a ghost effect system [Y. Sone, Kinetic Theory and Fluid Dynamics, Model. Simul. Sci. Eng. Technol., Birkhäuser, Boston, 2002]. Our analysis builds upon the framework developed by Métivier and Schochet [Arch. Ration. Mech. Anal., 158 (2001), pp. 61-90] and Alazard [Arch. Ration. Mech. Anal., 180 (2006), pp. 1-73] for nondispersive systems. The strategy involves establishing a priori estimates for the slow motion as well as a priori estimates for the fast motion. The desired convergence is obtained by establishing the local decay of the energy of the fast motion. [PUBLICATION ABSTRACT]