First Critical Field in the pinned three-dimensional Ginzburg--Landau Model: A matching upper bound
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_ | 1866912666569670656 |
|---|---|
| author | Román, Carlos |
| author_facet | Román, Carlos |
| contents | We continue our study of the first critical field $H_{c_1}$ for extreme type-II superconductors governed by the three-dimensional magnetic Ginzburg--Landau functional with a pinning term $a_\varepsilon$, as introduced in our previous work [arXiv:2507.10915]. Building upon the lower bound for $H_{c_1}$ and the characterization of the Meissner solution, we now establish a matching upper bound for $H_{c_1}$, thereby identifying its leading-order behavior. This result confirms the sharpness of the previously derived lower bound and further elucidates the connection between the onset of vorticity and a weighted variant of the \emph{isoflux problem}. Our argument is prompted by the upper bound construction we developed in [arXiv:2510.14910], based on the Biot--Savart law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First Critical Field in the pinned three-dimensional Ginzburg--Landau Model: A matching upper bound Román, Carlos Analysis of PDEs Mathematical Physics 35Q56, 35J20, 35B40, 82D55 We continue our study of the first critical field $H_{c_1}$ for extreme type-II superconductors governed by the three-dimensional magnetic Ginzburg--Landau functional with a pinning term $a_\varepsilon$, as introduced in our previous work [arXiv:2507.10915]. Building upon the lower bound for $H_{c_1}$ and the characterization of the Meissner solution, we now establish a matching upper bound for $H_{c_1}$, thereby identifying its leading-order behavior. This result confirms the sharpness of the previously derived lower bound and further elucidates the connection between the onset of vorticity and a weighted variant of the \emph{isoflux problem}. Our argument is prompted by the upper bound construction we developed in [arXiv:2510.14910], based on the Biot--Savart law. |
| title | First Critical Field in the pinned three-dimensional Ginzburg--Landau Model: A matching upper bound |
| topic | Analysis of PDEs Mathematical Physics 35Q56, 35J20, 35B40, 82D55 |
| url | https://arxiv.org/abs/2510.20720 |