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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2604.03519 |
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| _version_ | 1866908936437760000 |
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| author | Shahmurov, Rishad |
| author_facet | Shahmurov, Rishad |
| contents | We study axis regularity for the three-dimensional axisymmetric incompressible Navier--Stokes equations through a five-dimensional radial lift with weighted measure \[ dμ_5=r^3\,dr\,dz. \] In this formulation the axis problem is reduced to three weighted unit-cylinder estimates: a Hardy--Campanato decay estimate for the singular parabolic core, a weighted Friedrichs--Poincaré estimate for the renormalized vorticity branch, and a localized weighted quartic estimate for the swirl source. The distinguished corridor \[ α\in\left(\frac34,1\right) \] is the range singled out by the scaling analysis of the lifted problem. The main theorem is stated in unconditional form; the remaining unit-scale constants are treated as certified numerical inputs and are recorded in Appendix~A. The body of the paper presents the full analytic reduction from these weighted estimates to a contractive Morrey iteration at the axis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03519 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unconditional Axis-Regularity in the 5D Corridor Shahmurov, Rishad Analysis of PDEs We study axis regularity for the three-dimensional axisymmetric incompressible Navier--Stokes equations through a five-dimensional radial lift with weighted measure \[ dμ_5=r^3\,dr\,dz. \] In this formulation the axis problem is reduced to three weighted unit-cylinder estimates: a Hardy--Campanato decay estimate for the singular parabolic core, a weighted Friedrichs--Poincaré estimate for the renormalized vorticity branch, and a localized weighted quartic estimate for the swirl source. The distinguished corridor \[ α\in\left(\frac34,1\right) \] is the range singled out by the scaling analysis of the lifted problem. The main theorem is stated in unconditional form; the remaining unit-scale constants are treated as certified numerical inputs and are recorded in Appendix~A. The body of the paper presents the full analytic reduction from these weighted estimates to a contractive Morrey iteration at the axis. |
| title | Unconditional Axis-Regularity in the 5D Corridor |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.03519 |