Gevrey regularity solution for initial data in Triebel-Lizorkin-Lorentz spaces via single norm defined by nonlinearity of frequency
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914140021325824 |
|---|---|
| author | Yang, Qixiang Li, Hongwei |
| author_facet | Yang, Qixiang Li, Hongwei |
| contents | The properties of solutions to Navier-Stokes equations, including well-posedness and Gevrey regularity, are a class of highly interesting problems. We are inspired by the location result on Triebel-Lizorkin-Lorentz space of Hobus and Saal in 2019. In order to overcome the difficulties they encountered when dealing with global well-posedness, we introduce the single norm iterative space ${^{m'}_{m} \dot{F}}^{\frac{n}{p}-1,q}_{p,r}$ and utilize tools such as the Fefferman-Stein inequality to investigate the properties of our iterative spaces. As a result, we establish the global well-posedness of Navier-Stokes equations in critical Triebel-Lizorkin-Lorentz space and obtain the Gevrey regularity of the mild solution. Regarding that there're many regularity studies focused on Besov spaces, such as Bae-Biswas-Tadmor(2012) and Liu-Zhang (2024), our Triebel-Lizorkin-Lorentz spaces contain more general initial value spaces, including part of Besov spaces and all of Triebel-Lizorkin spaces, etc.. Furthermore, compared with Germain-Pavlović-Staffilani (2007), our Gevrey estimation also implies spatial analyticity and is more convenient to unify the estimates of gradient of any order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gevrey regularity solution for initial data in Triebel-Lizorkin-Lorentz spaces via single norm defined by nonlinearity of frequency Yang, Qixiang Li, Hongwei Analysis of PDEs 35Q30, 76D03, 42B35, 46E30 The properties of solutions to Navier-Stokes equations, including well-posedness and Gevrey regularity, are a class of highly interesting problems. We are inspired by the location result on Triebel-Lizorkin-Lorentz space of Hobus and Saal in 2019. In order to overcome the difficulties they encountered when dealing with global well-posedness, we introduce the single norm iterative space ${^{m'}_{m} \dot{F}}^{\frac{n}{p}-1,q}_{p,r}$ and utilize tools such as the Fefferman-Stein inequality to investigate the properties of our iterative spaces. As a result, we establish the global well-posedness of Navier-Stokes equations in critical Triebel-Lizorkin-Lorentz space and obtain the Gevrey regularity of the mild solution. Regarding that there're many regularity studies focused on Besov spaces, such as Bae-Biswas-Tadmor(2012) and Liu-Zhang (2024), our Triebel-Lizorkin-Lorentz spaces contain more general initial value spaces, including part of Besov spaces and all of Triebel-Lizorkin spaces, etc.. Furthermore, compared with Germain-Pavlović-Staffilani (2007), our Gevrey estimation also implies spatial analyticity and is more convenient to unify the estimates of gradient of any order. |
| title | Gevrey regularity solution for initial data in Triebel-Lizorkin-Lorentz spaces via single norm defined by nonlinearity of frequency |
| topic | Analysis of PDEs 35Q30, 76D03, 42B35, 46E30 |
| url | https://arxiv.org/abs/2509.15663 |