PreprintCC BY 4.0arXiv
Source-Driven Transitions in Axisymmetric Euler Flow
Abstract
We study a finite-time source-driven transition in axisymmetric Euler flow with swirl. For an explicit smooth compact datum, we prove exact source, moment-return, fixed-label transport, and response identities. For the same frozen finite reference, interval arithmetic gives continuum derivative bounds and a terminal scalar-trace enclosure. Under the remaining global comparison hypotheses, these estimates imply contraction of two fixed material labels and a finite-radius outgoing level set. We state separately the unresolved steps: global defect enclosure, sufficient next-block admission, cylindrical whole-space realization, and repeated regeneration from one datum. No whole-space Euler singularity is claimed
Related
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- Rough Axisymmetric Euler Dynamics: Global Energy Compactness and Kinetic Passage Across Regularity Breakdown
BibTeX
@misc{shahmurov2026sourcedriven,
title = {{Source-Driven Transitions in Axisymmetric Euler Flow}},
author = {Rishad Shahmurov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.04526},
eprint = {2605.04526},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04526},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Source-Driven Transitions in Axisymmetric Euler Flow
AU - Rishad Shahmurov
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.04526
UR - https://arxiv.org/abs/2605.04526
AB - We study a finite-time source-driven transition in axisymmetric Euler flow with swirl. For an explicit smooth compact datum, we prove exact source, moment-return, fixed-label transport, and response identities. For the same frozen finite reference, interval arithmetic gives continuum derivative bounds and a terminal scalar-trace enclosure. Under the remaining global comparison hypotheses, these estimates imply contraction of two fixed material labels and a finite-radius outgoing level set. We state separately the unresolved steps: global defect enclosure, sufficient next-block admission, cylindrical whole-space realization, and repeated regeneration from one datum. No whole-space Euler singularity is claimed
ER -