A connection between viscous profiles and singular ODEs

Details A connection between viscous profiles and singular ODEs A connection between viscous profiles and singular ODEs

2008-01-29

arxiv.org/abs/0801.4532v2

Mathematics

Analysis of PDEs

6 pages, minor changes

Scientific paper

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 $$ dV / dt = F(V) / z (V) . $$ Here $V \in R^d$ and the function F takes values into $R^d$ and is smooth. The real valued function z is as well regular: the equation is singular in the sense that z (V) can attain the value 0.

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