Endpoint Architectures for Navier--Stokes
Abstract
We compare two endpoint analyses for three-dimensional Navier--Stokes flow: a general suitable-weak framework and the axisymmetric equations with swirl. The common backend is selection of physical space--time records, nonoverlapping allocation of positive quantities, retention of the full localized state, and passage either to a compact transition law or to an explicitly named loss of compactness. The front-end theorems are different. In the general problem, bounded-critical sequences lead to symmetry/defect alternatives, while amplitude-fast normalization leads conditionally to an ancient Euler profile only after frequency tightness and a nonvanishing witness are retained. In the axisymmetric problem, logarithmic swirl records are routed to meridional energy or scale-critical signed compression, whereas first-use provenance and recharge packing force recurrent fresh service toward boundary, age, frequency, or other recession mechanisms. We state the interfaces and the remaining endpoints without identifying their currencies or reducing the general problem to the axisymmetric class. No unconditional regularity theorem or singularity construction is claimed.
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BibTeX
@misc{shahmurov2026endpoint,
title = {{Endpoint Architectures for Navier--Stokes}},
author = {Rishad Shahmurov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.09797},
eprint = {2605.09797},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.09797},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Endpoint Architectures for Navier--Stokes
AU - Rishad Shahmurov
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.09797
UR - https://arxiv.org/abs/2605.09797
AB - We compare two endpoint analyses for three-dimensional Navier--Stokes flow: a general suitable-weak framework and the axisymmetric equations with swirl. The common backend is selection of physical space--time records, nonoverlapping allocation of positive quantities, retention of the full localized state, and passage either to a compact transition law or to an explicitly named loss of compactness. The front-end theorems are different. In the general problem, bounded-critical sequences lead to symmetry/defect alternatives, while amplitude-fast normalization leads conditionally to an ancient Euler profile only after frequency tightness and a nonvanishing witness are retained. In the axisymmetric problem, logarithmic swirl records are routed to meridional energy or scale-critical signed compression, whereas first-use provenance and recharge packing force recurrent fresh service toward boundary, age, frequency, or other recession mechanisms. We state the interfaces and the remaining endpoints without identifying their currencies or reducing the general problem to the axisymmetric class. No unconditional regularity theorem or singularity construction is claimed.
ER -