Stable Finite-Time Singularity Formation for 3D Navier--Stokes via 5D-Lifted Axisymmetric Reductions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913022342070272 |
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| author | Shahmurov, Rishad |
| author_facet | Shahmurov, Rishad |
| contents | We present a 5D-lifted analytic-profile program for finite-time singularity formation in the 3D incompressible Navier--Stokes equations on the periodic torus $\T^3$. The core of the construction is a stationary rescaled profile $\Ombar$ satisfying a nonlinear elliptic fixed-point equation in an analytically weighted Hilbert space $\Xspace$, together with a computer-assisted Newton--Kantorovich validation based on interval arithmetic. The profile is reconstructed into a nearly self-similar singular evolution and then transferred to $\T^3$ by periodic extension and exact Leray projection. The manuscript is organized in the style of a computer-assisted proof paper, with theorem statements, proof packages, and explicit validation constants for the residual, inverse stability, and Lipschitz bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09949 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stable Finite-Time Singularity Formation for 3D Navier--Stokes via 5D-Lifted Axisymmetric Reductions Shahmurov, Rishad Analysis of PDEs We present a 5D-lifted analytic-profile program for finite-time singularity formation in the 3D incompressible Navier--Stokes equations on the periodic torus $\T^3$. The core of the construction is a stationary rescaled profile $\Ombar$ satisfying a nonlinear elliptic fixed-point equation in an analytically weighted Hilbert space $\Xspace$, together with a computer-assisted Newton--Kantorovich validation based on interval arithmetic. The profile is reconstructed into a nearly self-similar singular evolution and then transferred to $\T^3$ by periodic extension and exact Leray projection. The manuscript is organized in the style of a computer-assisted proof paper, with theorem statements, proof packages, and explicit validation constants for the residual, inverse stability, and Lipschitz bounds. |
| title | Stable Finite-Time Singularity Formation for 3D Navier--Stokes via 5D-Lifted Axisymmetric Reductions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.09949 |