Dispersive Corrections to the Compressible Navier-Stokes System
C. David Levermore, University of Maryland, College Park

Kinetic theory gives dispersive corrections to the compressible Navier-Stokes system of gas dynamics. The so-called dispersive Navier-Stokes system that arises dissipates the Euler entropy, and so seem  formally well-posed.  We give local well-posedness and smoothing results for classical solutions over the entire space that satisfy asymptotic flatness and nontrapping conditions.  Due to degeneracies in both the disspersion and dissipation of the system, different components of the solution gain different regularity.  The coupling of these components is analyzed using pseudodifferential operators.