旋转流体的整体适定性理论

The study find out that the typical amplitude of velocity in the ocean is a few meters per second (except in strong oceanic currents like the Gulf Stream), and the typical size of an ocean is 5000 kilometers. It therefore takes 50 days for a fluid particle to cross the ocean. Meanwhile the Earth has made 50 rotations. As a consequence, if we want to study oceans at a global level, the Coriolis force cannot be neglected. In the case of ignoring temperature, salinity, and stratification, the rotating fluids can represented by the Navier-Stokes equations with Coriolis force. In this project, we want to study the global existence result of the large solution for the rotating fluids under the condition that the roating velocity is large enough. More over, we will consider the large time behavior of the solution in the case of homogeneous and inhomogeneous fluids.

研究发现，海洋中一般的流速满足每秒几米(除非是像墨西哥暖流那样强烈的海洋洋流)并且，一般来说，海洋的跨度约为5000千米。由此可得，一个流体质点大概需要50天时间去横跨一个大洋。与此同时，地球也自转了50圈。因此，如果我们要去研究全球的海洋运动，Coriolis 力是不可忽略。在忽略温度、盐度以及分层的情况下， 旋转流体在数学上可以表示为带Coriolis外力项的Navier-Stokes方程。本课题将研究旋转流体在旋转速度充分大的情况下，存在整体大解。更进一步，我们将研究常密度与变密度情形下解的大时间行为。

研究发现，海洋中一般的流速满足每秒几米(除非是像墨西哥暖流那样强烈的海洋洋流)并且，一般来说，海洋的跨度约为5000千米。由此可得，一个流体质点大概需要50天时间去横跨一个大洋。与此同时，地球也自转了50圈。因此，如果我们要去研究全球的海洋运动，Coriolis 力是不可忽略。在忽略温度、盐度以及分层的情况下， 旋转流体在数学上可以表示为带Coriolis外力项的Navier-Stokes方程。本课题的研究内容分为两部分：一是当旋转速度充分大时，不可压Navier-Stokes-Coriolis方程的整体适定性理论；二是当旋转速度固定时，不可压Navier-Stokes-Coriolis方程的整体适定性理论