发表机构
Texas A&M University（德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对行星地转尺度下的三维Boussinesq方程，通过建立一致估计和新颖的无浮力流动分解方法，得到无初始数据限制的全局解，并严格证明其行星地转近似的合理性。
AI 中文摘要
我们研究行星地转尺度下的三维Boussinesq方程，其中浮力驱动的流动在大水平空间尺度下接近地转平衡。通过建立关于特征数的一致估计，我们能够得到Boussinesq方程的全局弱解和唯一全局强解，且对初始数据无限制。此外，通过将特征数取零并结合已建立的紧性，严格证明了Boussinesq方程的行星地转近似的合理性。我们采用新颖的无浮力流动分解方法来克服由浮力引起的奇异性。
英文摘要
We investigate the three dimensional Boussinesq equations in the planetary geostrophic scale, where the buoyancy/gravity driven flow is near geostrophic balance in the large horizontal spatial scale. By establishing the uniform (with respect to the characteristic number) estimates, we are able to obtain the global weak solutions and the unique global strong solutions to the Boussinesq equations without restriction on the initial data. Furthermore, sending the characteristic number to zero with the established compactness rigorously justifies the planetary geostrophic approximation of the Boussinesq equations. We employ the novel buoyancy flow-free flow decomposition to overcome the singularity caused by the buoyancy/gravity.
Comments20 pages, to be submitted to SIAM Journal on Mathematical Analysis, accepted in SIAM TXLA 2026
