Some questions about the regularity and the uniqueness of solutions of parabolic partial differential equations
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_ | 1866910972744040448 |
|---|---|
| author | Delgado, Inmaculada Gayte Gayte, Irene Marín |
| author_facet | Delgado, Inmaculada Gayte Gayte, Irene Marín |
| contents | This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the study of the sign of certain solutions to linear parabolic problems. This fixed-point equation implies regularity properties of solutions to parabolic problems, not necessarily linear, and this allows us to prove the uniqueness of the solution in three dimensions for the Navier-Stokes problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some questions about the regularity and the uniqueness of solutions of parabolic partial differential equations Delgado, Inmaculada Gayte Gayte, Irene Marín Analysis of PDEs 35Q30, 49K20, 76D05, 93C95 This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the study of the sign of certain solutions to linear parabolic problems. This fixed-point equation implies regularity properties of solutions to parabolic problems, not necessarily linear, and this allows us to prove the uniqueness of the solution in three dimensions for the Navier-Stokes problem. |
| title | Some questions about the regularity and the uniqueness of solutions of parabolic partial differential equations |
| topic | Analysis of PDEs 35Q30, 49K20, 76D05, 93C95 |
| url | https://arxiv.org/abs/2505.22110 |