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Floquet instability near a stationary Euler flow in 3D

  • Mimi Dai
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Abstract

We study the three-dimensional (3D) incompressible Euler equation linearized about a smooth compactly supported stationary flow of Gavrilov type. Baldi's volume-preserving action--angle chart allows a reduction of the high-frequency amplitude equation on invariant tori. Using Baldi's chart, we identify a critical torus ensured by the compact cutoff. We show that, for a fixed axisymmetric covector with sufficiently large normal component, the reduced trace-free periodic cocycle on this torus is hyperbolic and has a positive Floquet exponent. A localized geometric-optics construction then lifts this Floquet instability to the linearized Euler equation, yielding exponential essential-norm growth in space Hs, s≥ 0.

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Cite

BibTeXRIS
BibTeX
@misc{dai2026floquet,
  title = {{Floquet instability near a stationary Euler flow in 3D}},
  author = {Mimi Dai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.30401},
  eprint = {2609.30401},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.30401},
}
RIS
TY  - UNPB
TI  - Floquet instability near a stationary Euler flow in 3D
AU  - Mimi Dai
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.30401
UR  - https://arxiv.org/abs/2609.30401
AB  - We study the three-dimensional (3D) incompressible Euler equation linearized about a smooth compactly supported stationary flow of Gavrilov type. Baldi's volume-preserving action--angle chart allows a reduction of the high-frequency amplitude equation on invariant tori. Using Baldi's chart, we identify a critical torus ensured by the compact cutoff. We show that, for a fixed axisymmetric covector with sufficiently large normal component, the reduced trace-free periodic cocycle on this torus is hyperbolic and has a positive Floquet exponent. A localized geometric-optics construction then lifts this Floquet instability to the linearized Euler equation, yielding exponential essential-norm growth in space H^s, s≥ 0.
ER  -