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PreprintarXiv licencearXiv

Asymptotic stability of the 2D Boussinesq equations around Couette flow in infinite channel

  • Qionglei Chen
  • Jiakun Jin
  • Zhen Li
  • Changxing Miao
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Abstract

In this paper, we investigate the stability threshold of the two-dimensional Boussinesq system around the Couette flow in an infinite channel ℝ×[−1,1] under Navier-slip boundary condition. To address nonlinear echo chains induced by temperature-vorticity coupling, we construct a two-level frequency-dependent temporal decomposition, with the two levels matched to the infinite and finite superposition principles for the equation, respectively. By fully exploiting the enhanced dissipation effect at each decomposition level, we prove that if the initial perturbation (ωin, θin) around the Couette flow satisfies |ωin|H4x,y∩ L1xH4y≤ cν1/3, and |θin|H5x,y∩ L1xH5y≤ cν2/3+, the Boussinesq system admits a globally asymptotically stable solution. It should be emphasized that the method in this paper provides an effective approach for the hydrodynamic equations with coupling effects.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026asymptotic,
  title = {{Asymptotic stability of the 2D Boussinesq equations around Couette flow in infinite channel}},
  author = {Qionglei Chen and Jiakun Jin and Zhen Li and Changxing Miao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10005},
  eprint = {2610.10005},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10005},
}
RIS
TY  - UNPB
TI  - Asymptotic stability of the 2D Boussinesq equations around Couette flow in infinite channel
AU  - Qionglei Chen
AU  - Jiakun Jin
AU  - Zhen Li
AU  - Changxing Miao
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10005
UR  - https://arxiv.org/abs/2610.10005
AB  - In this paper, we investigate the stability threshold of the two-dimensional Boussinesq system around the Couette flow in an infinite channel ℝ×[−1,1] under Navier-slip boundary condition. To address nonlinear echo chains induced by temperature-vorticity coupling, we construct a two-level frequency-dependent temporal decomposition, with the two levels matched to the infinite and finite superposition principles for the equation, respectively. By fully exploiting the enhanced dissipation effect at each decomposition level, we prove that if the initial perturbation (ω^in, θ^in) around the Couette flow satisfies |ω^in|_H^4_x,y∩ L^1_xH^4_y≤ cν^1/3, and |θ^in|_H^5_x,y∩ L^1_xH^5_y≤ cν^2/3+, the Boussinesq system admits a globally asymptotically stable solution. It should be emphasized that the method in this paper provides an effective approach for the hydrodynamic equations with coupling effects.
ER  -