Entropy solutions in $BV^s$ for a class of triangular systems involving a transport equation
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_ | 1866929263844786176 |
|---|---|
| author | Bourdarias, Christian Choudhury, Anupam Pal Guelmame, Billel Junca, Stéphane |
| author_facet | Bourdarias, Christian Choudhury, Anupam Pal Guelmame, Billel Junca, Stéphane |
| contents | In this article, we consider a class of strictly hyperbolic triangular systems involving a transport equation. Such systems are known to create measure solutions for the initial value problem. Adding a stronger transversality assumption on the fields, we are able to obtain solutions in $L^\infty$ under optimal fractional $BV$ regularity of the initial data. Our results show that the critical fractional regularity is $s=1/3$. We also construct an initial data that is not in $BV^{1/3}$ but for which a blow-up in $L^\infty$ occurs, proving the optimality of our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16820 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entropy solutions in $BV^s$ for a class of triangular systems involving a transport equation Bourdarias, Christian Choudhury, Anupam Pal Guelmame, Billel Junca, Stéphane Analysis of PDEs In this article, we consider a class of strictly hyperbolic triangular systems involving a transport equation. Such systems are known to create measure solutions for the initial value problem. Adding a stronger transversality assumption on the fields, we are able to obtain solutions in $L^\infty$ under optimal fractional $BV$ regularity of the initial data. Our results show that the critical fractional regularity is $s=1/3$. We also construct an initial data that is not in $BV^{1/3}$ but for which a blow-up in $L^\infty$ occurs, proving the optimality of our results. |
| title | Entropy solutions in $BV^s$ for a class of triangular systems involving a transport equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.16820 |