发表机构
Institute of Applied Physics and Computational Mathematics; Graduate School of China Academy of Engineering Physics; Hefei University of Technology; University of Science and Technology Beijing（北京应用物理与计算数学研究所; 中国工程物理研究院研究生院; 合肥工业大学; 北京科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对无限通道中Couette流周围的二维Boussinesq系统，通过两层频率依赖时间分解和增强耗散效应，证明了在特定初始扰动条件下系统存在全局渐近稳定解。
AI 中文摘要
本文研究了在Navier-slip边界条件下，无限通道$\mathbb{R}\times[-1,1]$中Couette流周围二维Boussinesq系统的稳定性阈值。为处理温度-涡度耦合引起的非线性回声链，我们构建了一个两层频率依赖的时间分解，其中两层分别对应于方程的无限和有限叠加原理。通过充分利用每一分解层的增强耗散效应，我们证明了若Couette流周围的初始扰动$(\omega^{in}, \theta^{in})$满足$\\|\omega^{in}\\|_{H^4_{x,y}\cap L^1_xH^4_y}\leq c\nu^{\frac{1}{3}}$和$\\|\theta^{in}\\|_{H^5_{x,y}\cap L^1_xH^5_y}\leq c\nu^{\frac{2}{3}+}$，则Boussinesq系统存在全局渐近稳定解。需要强调的是，本文方法为具有耦合效应的流体动力学方程提供了有效途径。
英文摘要
In this paper, we investigate the stability threshold of the two-dimensional Boussinesq system around the Couette flow in an infinite channel $\mathbb{R}\times[-1,1]$ 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 $\|ω^{in}\|_{H^4_{x,y}\cap L^1_xH^4_y}\leq cν^{\frac{1}{3}}$, and $\|θ^{in}\|_{H^5_{x,y}\cap L^1_xH^5_y}\leq cν^{\frac{2}{3}+}$, 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.
