低Froude数区域下无量纲不可压Navier-斯托克斯方程解的整体存在性和收敛性
Global existence and convergence for non-dimensionalized incompressible Navier-Stokes equations in low Froude number regime
摘要：
我们证明了不可压缩的，密度相关的，Navier-斯托克斯方程的整体适定在低弗劳德数制度。密度应该在深度上增加，并在稳定状态附近线性化。此外，如果弗劳德数趋于零，我们证明了这样的系统（强）收敛到一个二维的，分层的Navier-Stokes方程组与全扩散。没有对初始数据进行小规模假设。
英文摘要：
We prove that the incompressible, density dependent, Navier-Stokes equations are globally well posed in a low Froude number regime. The density is supposed to be increasing in depth and linearized around a stable state. Moreover if the Froude number tends to zero we prove that such system converges (strongly) to a two-dimensional, stratified Navier-Stokes system with full diffusivity. No smallness assumption is made on the initial data.
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