Boussinesq方程温和解的全局适定性

Global Well-Posedness of the Mild Solutions to the Boussinesq Equations

Boussinesq方程作为描述许多地球物理现象的模型,是Navier-Stokes方程与热力学方程之间耦合的零阶近似.利用隐函数定理,研究带黏性高维Boussinesq系统,并得到了小初值位于尺度不变空间时温和解的全局适定性.

The Boussinesq system,as a model to describe many geophysical phenomena,is a zero-order approximation of the coupling between the Navier-Stokes equations and the thermodynamic equations.The multi-dimensional viscous Boussinesq equations were considered.By means of the implicit function theorem,the global well-posedness of the mild solutions was obtained with the small initial data in the scaling invariant spaces.