Global Stability of the Boltzmann Equation for a Polyatomic Gas with Initial Data Allowing Large Oscillations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917898946084864 |
|---|---|
| author | Ko, Gyounghun Son, Sung-jun |
| author_facet | Ko, Gyounghun Son, Sung-jun |
| contents | In this paper, we consider the Boltzmann equation for a polyatomic gas. We establish that the mild solution to the Boltzmann equation on the torus is globally well-posed, provided the initial data that satisfy bounded velocity-weighted $L^{\infty}$ norm and the smallness condition on the initial relative entropy. Furthermore, we also study the asymptotic behavior of solutions, converging to the global Maxwellian with an exponential rate. A key point in the proof is to develop the pointwise estimate on the gain term of non-linear collision operator for Grönwall's argument. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_13192 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Stability of the Boltzmann Equation for a Polyatomic Gas with Initial Data Allowing Large Oscillations Ko, Gyounghun Son, Sung-jun Analysis of PDEs 35Q20, 76P05 In this paper, we consider the Boltzmann equation for a polyatomic gas. We establish that the mild solution to the Boltzmann equation on the torus is globally well-posed, provided the initial data that satisfy bounded velocity-weighted $L^{\infty}$ norm and the smallness condition on the initial relative entropy. Furthermore, we also study the asymptotic behavior of solutions, converging to the global Maxwellian with an exponential rate. A key point in the proof is to develop the pointwise estimate on the gain term of non-linear collision operator for Grönwall's argument. |
| title | Global Stability of the Boltzmann Equation for a Polyatomic Gas with Initial Data Allowing Large Oscillations |
| topic | Analysis of PDEs 35Q20, 76P05 |
| url | https://arxiv.org/abs/2407.13192 |