Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.01159 |
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Inhaltsangabe:
- In this paper, we study the stability threshold of the two-dimensional Boussinesq equations around the Couette flow in an infinite channel $\mathbb{R} \times [-1, 1]$ under no-slip boundary conditions. We prove that the Couette flow is asymptotically stable under initial perturbations satisfying $\| \mathbf{v}^{\mathrm{in}} -(y,0)\|_{H^2} \le \varepsilon_0 ν^{\frac12}$, and $\| ρ^{\mathrm{in}}-1 \|_{H^1} + \big\| |\partial_x|^{\frac13} ρ^{\mathrm{in}} \big\|_{H^1} \le \varepsilon_1 ν^{\frac56}$. Compared with the work of Masmoudi, Zhai, and Zhao [J. Funct. Anal., 284 (2023), 109736], where the asymptotic stability of the 2D Navier-Stokes-Boussinesq system around Couette flow in a finite channel $\mathbb{T} \times [-1, 1]$ was established, our result improves the stability threshold for the temperature from $ν^{\frac{11}{12}}$ to $ν^{\frac56}$.