Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids
Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids
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DOI：
10.1090/memo/1073
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发表时间：
2014-03
期刊：
影响因子：
--
通讯作者：
Hajime Koba
中科院分区：
文献类型：
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作者：
Hajime Koba
带有边界条件的旋转Navier-Stokes方程的定常解称为Ekman边界层。这本小册子构造了旋转的Navier-Stokes-Boussinesq方程的定态解，在旋转轴不一定垂直于地平线的情况下具有分层效应。我们称这种稳定的解决方案埃克曼层。这本小册子展示了一个Ekman扰动系统的弱解的存在性，它满足强能量不等式。在对Ekman层和物理参数的一些假设下，讨论了弱解的唯一性，并计算了弱解随时间的衰减率。当初值足够小时，扰动系统存在唯一的时间上全局强解。将满足强能量不等式的弱解与强解进行比较，表明当时间足够大时，弱解关于时间是光滑的。
A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This booklet constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. We call such stationary solutions Ekman layers. This booklet shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, we discuss the uniqueness of weak solutions and compute the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. It is also shown that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.