Stability threshold of the Couette flow in 2D Navier-Stokes Boussinesq equations on 𝕋 × [−1, 1] and ℝ × [−1, 1]

@misc{zhang2026stability,
  title = {{Stability threshold of the Couette flow in 2D Navier-Stokes Boussinesq equations on $\mathbbT \times [-1, 1]$ and $\mathbbR \times [-1, 1]$}},
  author = {Nangao Zhang and Gengwei Zhong and Ruizhao Zi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12810},
  eprint = {2610.12810},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12810},
  note = {CC0},
}

TY  - UNPB
TI  - Stability threshold of the Couette flow in 2D Navier-Stokes Boussinesq equations on 𝕋 × [−1, 1] and ℝ × [−1, 1]
AU  - Nangao Zhang
AU  - Gengwei Zhong
AU  - Ruizhao Zi
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2610.12810
UR  - https://arxiv.org/abs/2610.12810
AB  - In this paper, we study the transition threshold problem for the 2D Navier-Stokes Boussinesq equations around the Couette flow with a constant background temperature in two domains: 𝕋 × [−1, 1] and ℝ × [−1, 1]. It was proved that if the sizes of initial perturbations of the vorticity and the temperature in Sobolev spaces are ν^fr13 and ν^fr56, respectively, then this system admits a globally stable solution. Besides, we derive the enhanced dissipation estimate for the vorticity and temperature, as well as the inviscid damping estimate for the velocity. The coupling in the equations poses some difficulties to the analysis. We overcome these challenges and establish the results via the quasi-linear method and energy estimates.
ER  -