Self-similar finite-time blowups with smooth profiles of the generalized Constantin-Lax-Majda model
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913482256941056 |
|---|---|
| author | Huang, De Qin, Xiang Wang, Xiuyuan Wei, Dongyi |
| author_facet | Huang, De Qin, Xiang Wang, Xiuyuan Wei, Dongyi |
| contents | We show that the $a$-parameterized family of the generalized Constantin-Lax-Majda model, also known as the Okamoto-Sakajo-Wunsch model, admits exact self-similar finite-time blowup solutions with interiorly smooth profiles for all $a\leq 1$. Depending on the value of $a$, these self-similar profiles are either smooth on the whole real line or compactly supported and smooth in the interior of their closed supports. The existence of these profiles is proved in a consistent way by considering the fixed-point problem of an $a$-dependent nonlinear map, based on which detailed characterizations of their regularity, monotonicity, and far-field decay rates are established. Our work unifies existing results for some discrete values of $a$ and also explains previous numerical observations for a wide range of $a$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_05895 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Self-similar finite-time blowups with smooth profiles of the generalized Constantin-Lax-Majda model Huang, De Qin, Xiang Wang, Xiuyuan Wei, Dongyi Analysis of PDEs Functional Analysis 35A21, 35Q31, 35C06, 34A34, 47H10 We show that the $a$-parameterized family of the generalized Constantin-Lax-Majda model, also known as the Okamoto-Sakajo-Wunsch model, admits exact self-similar finite-time blowup solutions with interiorly smooth profiles for all $a\leq 1$. Depending on the value of $a$, these self-similar profiles are either smooth on the whole real line or compactly supported and smooth in the interior of their closed supports. The existence of these profiles is proved in a consistent way by considering the fixed-point problem of an $a$-dependent nonlinear map, based on which detailed characterizations of their regularity, monotonicity, and far-field decay rates are established. Our work unifies existing results for some discrete values of $a$ and also explains previous numerical observations for a wide range of $a$. |
| title | Self-similar finite-time blowups with smooth profiles of the generalized Constantin-Lax-Majda model |
| topic | Analysis of PDEs Functional Analysis 35A21, 35Q31, 35C06, 34A34, 47H10 |
| url | https://arxiv.org/abs/2305.05895 |