论文标题
大规模潮湿气氛系统的全球适应性，仅在动态方程中具有水平粘度
Global well-posedness of large scale moist atmosphere system with only horizontal viscosity in the dynamic equation
论文作者
论文摘要
为了找到一个更好的物理模型来描述大规模的云水转化和降雨，我们考虑了一个潮湿的气氛模型，该模型由动态方程中的原始方程组成，其中仅具有水平粘度，以及描述水蒸气，雨水和云冷凝水的一组湿度方程。为了克服由于动态方程中缺乏垂直粘度而造成的困难，我们通过将粘性消除方法和$ z- $弱的解决方案方法结合并使用广义的Bihari-lasalle不平等来获得$ h^{1} $空间的本地存在。然后，在更高的初始数据假设下，我们将获得$ v $的全球存在。反过来，获得了整个系统的准长和强大解决方案。通过适当地引入两个新的未知数量，并利用单调操作员理论来克服由源术语中的重质功能引起的困难，我们获得了解决方案的唯一性。
In order to find a better physical model to describe the large-scale cloud-water transformation and rainfall, we consider a moist atmosphere model consisting of the primitive equations with only horizontal viscosity in the dynamic equation and a set of humidity equations describing water vapor, rain water and cloud condensates. To overcome difficulties caused by the absence of vertical viscosity in the dynamic equation, we get the local existence of $v$ in $H^{1}$ space by combining the viscous elimination method and the $z-$weak solution method and using the generalized Bihari-Lasalle inequality. And then, we get the global existence of $v$ under higher regularity assumption of initial data. In turn, the existence of quasi-strong and strong solutions to the whole system is obtained. By introducing two new unknown quantities appropriately and utilizing the monotone operator theory to overcome difficulties caused by the Heaviside function in the source terms, we get the uniqueness of solutions.
