Boundary Hyperbolic Packets in Axisymmetric Euler Flow
Abstract
We study hyperbolic side-wall packets for the axisymmetric Euler equations with swirl in a periodic cylinder. In the exact odd class, Γ=ruθ and G=ωθ/r satisfy DtΓ=0 and DtG=r−4∂z(Γ2), and the symmetry fixes the boundary point at which the relevant swirl and vorticity gradients are measured. We derive the five-dimensional side-wall Green-kernel expansion, its leading signed hyperbolic kernel, packet--core coupling, off-diagonal shear estimates, anisotropy and source-curvature identities, and a maximal conic-score formulation. Under a common admissible packet bootstrap these estimates imply the Dini system D+M≥ cB2, B'≥ cM B, and hence finite-time blow-up of the comparison amplitudes. The result is a conditional amplification criterion: it does not prove that one smooth Euler trajectory preserves all packet-dominance, tail, shear, anisotropy, and validity hypotheses until the comparison blow-up time. Establishing or refuting that persistence is the remaining problem for this mechanism.
Related
- Source-Driven Transitions in Axisymmetric Euler Flow
- Cavity collapse and kinetic energy concentration in three-dimensional free-boundary Euler flow
- A double-logarithmic lifespan bound for axisymmetric Euler equations with a small initial swirl
- Regularity for axisymmetric Navier-Stokes with an Euler length
- Vorticity growth beyond bounded relative vorticity for axisymmetric Euler flows without swirl
BibTeX
@misc{shahmurov2026boundary,
title = {{Boundary Hyperbolic Packets in Axisymmetric Euler Flow}},
author = {Rishad Shahmurov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.04181},
eprint = {2605.04181},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04181},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Boundary Hyperbolic Packets in Axisymmetric Euler Flow
AU - Rishad Shahmurov
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2605.04181
UR - https://arxiv.org/abs/2605.04181
AB - We study hyperbolic side-wall packets for the axisymmetric Euler equations with swirl in a periodic cylinder. In the exact odd class, Γ=ru^θ and G=ω^θ/r satisfy D_tΓ=0 and D_tG=r^−4∂_z(Γ^2), and the symmetry fixes the boundary point at which the relevant swirl and vorticity gradients are measured. We derive the five-dimensional side-wall Green-kernel expansion, its leading signed hyperbolic kernel, packet--core coupling, off-diagonal shear estimates, anisotropy and source-curvature identities, and a maximal conic-score formulation. Under a common admissible packet bootstrap these estimates imply the Dini system D^+M≥ cB^2, B'≥ cM B, and hence finite-time blow-up of the comparison amplitudes. The result is a conditional amplification criterion: it does not prove that one smooth Euler trajectory preserves all packet-dominance, tail, shear, anisotropy, and validity hypotheses until the comparison blow-up time. Establishing or refuting that persistence is the remaining problem for this mechanism.
ER -