2025/08/16 by Chen, Yubo, Wang, Wendong, Yang, Guoxu · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2508.11908
This paper establishes the asymptotic stability threshold for the Couette flow (y,0) under the 2D Boussinesq system in ℝ2. It was proved that for initial perturbations in Sobolev spaces with controlled low horizontal frequencies, the stability threshold is at most \(1)/(3)+, (2)/(3)+\, extending the known threshold results from the periodic case \mathbbTx × ℝy to the whole space. The core innovations are twofold: First, the ⟨ Dx-1 ⟩ control on the initial data simultaneously resolves horizontal frequency singularities and optimizes integral indices when applying Young's convolution inequality. Second, we develop a modified multiplier M3 that effectively absorbs the |Dx|1/3 derivative structure induced by the temperature equation while handling nonlinear echo cascades.