From nonisothermal BGK to Euler Maxwellians via relative entropy
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_ | 1866910075765915648 |
|---|---|
| author | Alves, Nuno J. |
| author_facet | Alves, Nuno J. |
| contents | We study the hydrodynamic limit of the nonisothermal BGK model toward smooth Euler Maxwellians. For a prescribed smooth Euler solution, we derive a relative entropy stability estimate between a BGK solution and the associated Maxwellian. The main new ingredient is the control of an additional velocity-cubic term in the relative entropy identity. Under a uniform sixth velocity-moment bound and suitable bounds on the BGK macroscopic quantities, we obtain a uniform-in-time relative entropy estimate. For well-prepared initial data, this yields strong $L^1$ convergence of the BGK solution and the local Maxwellians to the target Euler Maxwellian, together with convergence of the associated macroscopic quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_25487 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From nonisothermal BGK to Euler Maxwellians via relative entropy Alves, Nuno J. Analysis of PDEs We study the hydrodynamic limit of the nonisothermal BGK model toward smooth Euler Maxwellians. For a prescribed smooth Euler solution, we derive a relative entropy stability estimate between a BGK solution and the associated Maxwellian. The main new ingredient is the control of an additional velocity-cubic term in the relative entropy identity. Under a uniform sixth velocity-moment bound and suitable bounds on the BGK macroscopic quantities, we obtain a uniform-in-time relative entropy estimate. For well-prepared initial data, this yields strong $L^1$ convergence of the BGK solution and the local Maxwellians to the target Euler Maxwellian, together with convergence of the associated macroscopic quantities. |
| title | From nonisothermal BGK to Euler Maxwellians via relative entropy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.25487 |