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

초록

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 Hδ(R2)×Hs(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 Hm(R2), m∈N and in H˙m−1(R2) with m∈N, m≥2, respectively. © 2024 Elsevier Inc.

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