Abstract

In this thesis we develop tools for carrying out computer assisted proof of the stability of traveling wave solutions of the spatially one-dimensional compressible Navier-Stokes equations with an ideal gas equation of state. In particular, we obtain rigorous, tight error bounds on a high-accuracy numerical approximation of the traveling wave profile for parameters corresponding to air, and we obtain rigorous representations in a neighborhood of positive and negative infinity of the solution to the first order ODE associated with linearizing the PDE equations about the traveling wave solution. We also develop supporting tools for rigorous verification of wave stability.

Degree

College and Department

Computational, Mathematical, and Physical Sciences; Mathematics Education

Rights

https://lib.byu.edu/about/copyright/