论文标题
污染气氛的原始方程是3D Navier-Stokes方程的弱和强限制的下风匹配坐标
The primitive equations of the polluted atmosphere as a weak and strong limit of the 3D Navier-Stokes equations in downwind-matching coordinates
论文作者
论文摘要
一种广泛使用的方法来描述大气是将其视为浅域中的地球物理流体，因此，使用经典的流体动力学方程与明确包含ε参数代表物理领域的小长宽比相结合。在我们的上一篇论文[15]中，我们证明了较弱的收敛定理，用于通过对流扩散方程扩展的Navier-Stokes方程所描述的污染气氛。我们获得了普遍的静液压极限模型的理由，包括针对经典的，东北向上定向的当地笛卡尔坐标所描述的污染效应。在这里，我们对此声明进行了两倍的改进。首先，我们考虑一个在气象学上更有意义的坐标系，将这种坐标变化的分析后果纳入管理方程式，并验证弱收敛是否仍然适用于此更改的系统。其次，仍然考虑了这个新的，所谓的下风匹配坐标系，我们证明了类似的强收敛结果，我们还通过提供紧密相关的存在定理来完成。
A widely used approach to mathematically describe the atmosphere is to consider it as a geophysical fluid in a shallow domain -- and thus to model it using classical fluid dynamical equations combined with the explicit inclusion of an ε parameter representing the small aspect ratio of the physical domain. In our previous paper [15] we proved a weak convergence theorem for the polluted atmosphere described by the Navier-Stokes equations extended by an advection-diffusion equation. We obtained a justification of the generalised hydrostatic limit model including the pollution effect described for the case of classical, east-north-upwards oriented local Cartesian coordinates. Here we give a two-fold improvement of this statement. Firstly, we consider a meteorologically more meaningful coordinate system, incorporate the analytical consequences of this coordinate change into the governing equations, and verify that the weak convergence still holds for this altered system. Secondly, still considering this new, so-called downwind-matching coordinate system, we prove an analogous strong convergence result, which we make complete by providing a closely related existence theorem as well.
