Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems
Analysis of PDEs
2024-04-30 v1
Abstract
In the first part of this article we present some exact solutions for special hyperbolic-parabolic systems with sustained oscillations induced by the initial data, most notably the compressible Navier-Stokes system with non-monotone pressure. This part complements \cite{Tzavaras23} where such examples are extensively studied. The second part deals with the problem of homogenization for one-dimensional models describing phase transitions for viscoelastic materials . Ideas from the kinetic formulation of conservation laws are employed to derive effective equations that describe the propagation of oscillations.
Cite
@article{arxiv.2404.18455,
title = {Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems},
author = {Athanasios E. Tzavaras},
journal= {arXiv preprint arXiv:2404.18455},
year = {2024}
}