论文标题
关于可压缩各向异性Navier-Stokes方程的静静力近似 - 严格的理由
On the hydrostatic approximation of compressible anisotropic Navier-Stokes equations -- rigorous justification
论文作者
论文摘要
在这项工作中，我们通过将较小的纵横比限制限制到Navier-Stokes方程来获得静液压近似。纵横比（深度与水平宽度的比率）是一般的大尺度地球物理运动中的几何约束，垂直尺度明显小于水平。我们使用多功能的相对熵不等式来严格证明可压缩的Navier-Stokes方程到可压缩原始方程的极限。这是第一项使用相对熵不平等的工作来证明静水近似并得出可压缩原始方程。
In this work, we obtain the hydrostatic approximation by taking the small aspect ratio limit to the Navier-Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in general large scale geophysical motions that the vertical scale is significantly smaller than horizontal. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations to the compressible Primitive Equations. This is the first work to use relative entropy inequality for proving hydrostatic approximation and derive the compressible Primitive Equations.
