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PreprintCC0arXiv

Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations

  • Nangao Zhang
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Abstract

We study the transition threshold problem for the 2D Navier--Stokes Boussinesq equations around the Poiseuille flow on three domains: 𝕋 × ℝ, 𝕋 × [0, ∞), and 𝕋 × [−1, 1]. More precisely, we prove that if the initial perturbations of the vorticity and the temperature are assumed size O(min{νfr34,μfr34,ν−fr14μ}) and O(min{νfr94,μfr94}) in an anisotropic Sobolev space respectively, then for the solution to this system, its size remains so for all time, and the nonlinear enhanced dissipation persists with a rate proportional to O(min{νfr12,μfr12}).

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026stability,
  title = {{Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations}},
  author = {Nangao Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.07598},
  eprint = {2610.07598},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.07598},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Stability threshold of the Poiseuille flow in 2D Navier-Stokes Boussinesq equations
AU  - Nangao Zhang
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.07598
UR  - https://arxiv.org/abs/2610.07598
AB  - We study the transition threshold problem for the 2D Navier--Stokes Boussinesq equations around the Poiseuille flow on three domains: 𝕋 × ℝ, 𝕋 × [0, ∞), and 𝕋 × [−1, 1]. More precisely, we prove that if the initial perturbations of the vorticity and the temperature are assumed size O(min{ν^fr34,μ^fr34,ν^−fr14μ}) and O(min{ν^fr94,μ^fr94}) in an anisotropic Sobolev space respectively, then for the solution to this system, its size remains so for all time, and the nonlinear enhanced dissipation persists with a rate proportional to O(min{ν^fr12,μ^fr12}).
ER  -