Oscillations in Compressible Navier-Stokes and Homogenization in Phase Transition problems

2024/04/29 by Athanasios E. Tzavaras, Tzavaras, Athanasios E. · 1 citation
Computer Science · Engineering · Mathematics · #35Q30 76N10 35L60 74H35 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2404.18455

openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeTzavaras23 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.

Cited by

• Effective Equations for a Compressible Liquid-Vapor Flow Model with Highly Oscillating Initial Density

Related

• Sustained Oscillations in Hyperbolic-Parabolic Systems
• Homogenisation of parabolic/hyperbolic media
• The mathematical theory of splitting-merging patterns in phase transition dynamics
• Diffusion wave phenomena and L^p decay estimates of solutions of compressible viscoelastic system
• Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues