A LOW MACH NUMBER LIMIT OF A DISPERSIVE NAVIER-STOKES SYSTEM

作者：Levermore C David^*; Sun Weiran; Trivisa Konstantina

来源：SIAM Journal on Mathematical Analysis, 2012, 44(3): 1760-1807.

DOI：10.1137/100818765

• low Mach number
• compressible and viscous fluid
• dispersive Navier-Stokes equations
• kinetic theory
• ghost effect systems

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., Birkhauser, Boston, 2002]. Our analysis builds upon the framework developed by Metivier 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.

• 出版日期2012