A connection between viscous profiles and singular ODEs

2008/01/29 by Stefano Bianchini, Bianchini, Stefano, Laura V. Spinolo +1
Engineering · Mathematics · #34A99 #35L65 #35M10 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #math.CA #msc:34A99 #msc:35L65 #msc:35M10

paper · pdf · doi:10.48550/arxiv.0801.4532

6 pages, minor changes

openalex publication_date 2008/01/29 · arxiv created 2009/04/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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) / z (V) . Here V ∈ 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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