Forward Self-Similar Solutions to the 2D Hypodissipative Navier-Stokes Equations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914390321659904 |
|---|---|
| author | Hou, Thomas Y. Song, Peicong |
| author_facet | Hou, Thomas Y. Song, Peicong |
| contents | We study the forward self-similar solutions to the $2$D hypodissipative Navier-Stokes equation with fractional diffusion $(-Δ)^α$ for $\frac{1}{2}<α<1$. We first show that for arbitrarily large $(1-2α)$-homogeneous initial data which are locally Lipschitz, there exists at least one weak solution whose profile differs from the self-similar profile of the fractional heat equation by an element of $H^α(\mathbb{R}^2)$. Moreover, when $α\in(\frac{2}{3},1)$ we show that any such weak solution is actually smooth, hence a strong solution, and satisfies certain far field decay estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12497 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Forward Self-Similar Solutions to the 2D Hypodissipative Navier-Stokes Equations Hou, Thomas Y. Song, Peicong Analysis of PDEs Mathematical Physics Functional Analysis We study the forward self-similar solutions to the $2$D hypodissipative Navier-Stokes equation with fractional diffusion $(-Δ)^α$ for $\frac{1}{2}<α<1$. We first show that for arbitrarily large $(1-2α)$-homogeneous initial data which are locally Lipschitz, there exists at least one weak solution whose profile differs from the self-similar profile of the fractional heat equation by an element of $H^α(\mathbb{R}^2)$. Moreover, when $α\in(\frac{2}{3},1)$ we show that any such weak solution is actually smooth, hence a strong solution, and satisfies certain far field decay estimates. |
| title | Forward Self-Similar Solutions to the 2D Hypodissipative Navier-Stokes Equations |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2603.12497 |