Derivation of effective kinetic equations describing oscillations in viscoelasticity and in compressible Navier-Stokes
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913032933736448 |
|---|---|
| author | Tzavaras, Athanasios E. |
| author_facet | Tzavaras, Athanasios E. |
| contents | These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving double well potentials, as employed in phase transitions. (ii) The compressible Navier-Stokes equations for a barotropic gas. For each system we construct solutions with persistent oscillations. In a later part we consider the nonlinear homogenization problem. For the systems of viscoelasticity in one-space dimension in Lagrangian coordinates, and for the compressible Navier-Stokes system for barotropic fluids we show how ideas from the kinetic formulation of conservation laws can be used to derive effective equations. The effective equation consists by a kinetic equation coupled with the macroscopic flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_13330 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Derivation of effective kinetic equations describing oscillations in viscoelasticity and in compressible Navier-Stokes Tzavaras, Athanasios E. Analysis of PDEs 35L65, 35M30, 76N06 These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving double well potentials, as employed in phase transitions. (ii) The compressible Navier-Stokes equations for a barotropic gas. For each system we construct solutions with persistent oscillations. In a later part we consider the nonlinear homogenization problem. For the systems of viscoelasticity in one-space dimension in Lagrangian coordinates, and for the compressible Navier-Stokes system for barotropic fluids we show how ideas from the kinetic formulation of conservation laws can be used to derive effective equations. The effective equation consists by a kinetic equation coupled with the macroscopic flow. |
| title | Derivation of effective kinetic equations describing oscillations in viscoelasticity and in compressible Navier-Stokes |
| topic | Analysis of PDEs 35L65, 35M30, 76N06 |
| url | https://arxiv.org/abs/2604.13330 |