论文标题
快速旋转可压缩流体动力学中各向异性和分层效应
Anisotropy and stratification effects in the dynamics of fast rotating compressible fluids
论文作者
论文摘要
本文的主要目的是开发强大的方法来处理地球物理流的建模中出现的两个普遍特征：（i）粘性应力张量的各向异性，（ii）分层效应。我们专注于带有科里奥利和重力力的正压纳维尔 - 螺旋形方程。两个结果是本文的主要贡献。首先，我们通过最大的规律性方法为有限能源溶液建立了局部良好的结果。这种方法使我们能够规避使用有效的粘性通量的使用，这在狮子会和霍夫的弱解决方案理论中起着关键作用，但似乎仅限于各向同性粘性应力张量。此外，我们的方法足够坚固，可以考虑到非恒定的参考密度状态。在处理分层效应时，这至关重要。其次，当Rossby，Mach和Froude数量的数量级相同时，我们研究了制度中先前模型的解决方案的结构。我们证明了对实际解之间的相对熵及其近似之间的误差估计，并通过补充了Ekman边界层的大规模准地藻流量。我们的分析适用于大量的压力压力定律。
The primary goal of this paper is to develop robust methods to handle two ubiquitous features appearing in the modeling of geophysical flows: (i) the anisotropy of the viscous stress tensor, (ii) stratification effects. We focus on the barotropic Navier-Stokes equations with Coriolis and gravitational forces. Two results are the main contributions of the paper. Firstly, we establish a local well-posedness result for finite-energy solutions, via a maximal regularity approach. This method allows us to circumvent the use of the effective viscous flux, which plays a key role in the weak solutions theories of Lions-Feireisl and Hoff, but seems to be restricted to isotropic viscous stress tensors. Moreover, our approach is sturdy enough to take into account non constant reference density states; this is crucial when dealing with stratification effects. Secondly, we study the structure of the solutions to the previous model in the regime when the Rossby, Mach and Froude numbers are of the same order of magnitude. We prove an error estimate on the relative entropy between actual solutions and their approximation by a large-scale quasi-geostrophic flow supplemented with Ekman boundary layers. Our analysis holds for a large class of barotropic pressure laws.
