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July 30, 2026Journal of Fluid MechanicsOpen Access

Singularity of the axisymmetric stagnation-point-like solution within a cylinder of the 3-D Euler incompressible fluid equations

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Authors

YXYinshen XuMBMiguel D. Bustamante

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Overview

Analytical investigation of singularity formation in incompressible fluid under axisymmetric conditions, highlighting geometric influences.

Key Points

  • The aim is to analyze finite time singularities in 3-D incompressible Euler equations using the Gibbon–Fokas–Doering model.
  • Derivation of explicit Lagrangian solutions for vorticity and velocity components.
  • Analysis of local geometric structures influencing singularity formation.
  • Identification of critical thresholds for power law behavior near vortex stretching minima.
  • Existence of singularities is exclusively dependent on the local geometric structure of the initial vortex stretching rate.
  • Flatter profiles of the stretching rate delay singularity formation or may suppress it entirely.
  • Different thresholds for regular and singular solutions are identified, varying by location of singularity within the cylinder.

Cite This Study

Xu et al. (2026) studied this question.

synapsesocial.com/papers/6a6af4ad60e2b924d3ea02dahttps://doi.org/10.1017/jfm.2026.11847
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