Global well-posedness and stability of the 2D Boussinesq equations with partial dissipation near a hydrostatic equilibrium

2023/06/14 by Kyungkeun Kang, Jihoon Lee, Kang, Kyungkeun +3
Engineering · Mathematics · #35B35 #35Q35 #76D03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2306.08286

openalex publication_date 2023/06/14 · openalex created_date 2023/06/17 · openalex updated_date 2026/07/28

Abstract

The paper is devoted to investigating the well-posedness, stability and large-time behavior near the hydrostatic balance for the 2D Boussinesq equations with partial dissipation. More precisely, the global well-posedness is obtained in the case of partial viscosity and without thermal diffusion for the initial data belonging to H^δ(ℝ²) × H^s(ℝ²) for δ∈ [s-1,s+1] if s ∈ ℝ, s > 2, for δ∈ (1,s+1] if s ∈ (0,2] and for δ∈ [0,1] if s = 0. In addition, if one has either horizontal or vertical thermal diffusion then the stability and large-time behavior are provided in H^m(ℝ²), m ∈ ℕ and in H^m-1(ℝ²) with m ∈ ℕ, m ≥ 2, respectively.

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