A connection between viscous profiles and singular ODEs
Stefano Bianchini and Laura V. Spinolo
Abstract: We deal with the viscous profiles for a class of mixed hyperbolic–parabolic systems. We focus, in particular, on the case of the compressible Navier Stokes equation in one space variable written in Eulerian coordinates. We describe the link between these profiles and a singular ordinary differential equation in the form
dV/dt = F(V)/ζ(V).
Here V is in Rd and the function F takes values into Rd and is smooth. The real valued function ζ is as well regular: the equation is singular in the sense that ζ(V) can attain the value 0.