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.