The Muskat problem with a large slope
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_ | 1866916487692812288 |
|---|---|
| author | Xu, Yiran Cameron, Stephen Chen, Ke Hu, Ruilin Nguyen, Quoc-Hung |
| author_facet | Xu, Yiran Cameron, Stephen Chen, Ke Hu, Ruilin Nguyen, Quoc-Hung |
| contents | In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity \(β_σ(f_0')\) which encapsulates local monotonicity and slope, we identify a new class of initial data within \(W^{1,\infty}(\mathbb{R}^d)\). This includes scenarios where the product of the maximal and minimal slopes is large, thereby guaranteeing the local existence of a classical solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Muskat problem with a large slope Xu, Yiran Cameron, Stephen Chen, Ke Hu, Ruilin Nguyen, Quoc-Hung Analysis of PDEs In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity \(β_σ(f_0')\) which encapsulates local monotonicity and slope, we identify a new class of initial data within \(W^{1,\infty}(\mathbb{R}^d)\). This includes scenarios where the product of the maximal and minimal slopes is large, thereby guaranteeing the local existence of a classical solution. |
| title | The Muskat problem with a large slope |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2411.01501 |