Global well-posedness for dissipative IPM with data close to a class of special solutions
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913661776297984 |
|---|---|
| author | Zou, Liangchen |
| author_facet | Zou, Liangchen |
| contents | In this paper, we consider the 2-D dissipative incompressible porous media (IPM) equation in both supercritical and subcritical cases. The dissipative IPM equation admits a class of special solutions of the form $ρ(x_1,x_2,t)=f(x_2,t)$, which decay in the mode of the 1-D fractional heat equation. Our main result is the global well-posedness for the dissipative IPM equation with initial data close to this class of special solutions provided that $f$ satisfies certain regularity assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for dissipative IPM with data close to a class of special solutions Zou, Liangchen Analysis of PDEs In this paper, we consider the 2-D dissipative incompressible porous media (IPM) equation in both supercritical and subcritical cases. The dissipative IPM equation admits a class of special solutions of the form $ρ(x_1,x_2,t)=f(x_2,t)$, which decay in the mode of the 1-D fractional heat equation. Our main result is the global well-posedness for the dissipative IPM equation with initial data close to this class of special solutions provided that $f$ satisfies certain regularity assumptions. |
| title | Global well-posedness for dissipative IPM with data close to a class of special solutions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.13248 |