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

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-delta(R-2) x H-s(R-2) for delta is an element of [s - 1 , s + 1] if s is an element of R , s > 2, for delta is an element of (1 , s + 1] if s is an element of (0 , 2] and for delta is an element of [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(R-2) , m is an element of N and in Hm-1(R-2) with m is an element of N, m >= 2, respectively. (c) 2024 Elsevier Inc. All rights reserved.