无热耗散d维热带气候模型的小初值整体解

Global Small Solutions for the d-D Tropical Climate Model Without Thermal Diffusion

本文研究小初值情况下无热耗散d(d≥2)维热带气候模型的整体适定性问题,文中考虑的模型在速度的正压模和第一斜压模方程上分别具有分数阶耗散Λ^(2α)u的Λ^(2β)v.当0≤α<1,1/2≤β≤1且α+β≥1时,在小初值的假设下,我们建立了整体解的存在性和唯一性.

This paper studies the global well-posedness issue on the d-dimensional(d≥2)tropical climate model without thermal diffusion for small initial data.The model considered here has fractional dissipationsΛ^(2α)u andΛ^(2β)v on the equations of the barotropic mode and the first baroclinic mode of velocity,respectively.We establish the global existence and uniqueness of the solutions for the case when O≤α<1,1/2≤β≤1 andα+β≥1under small initial data.