The strong solutions to the primitive equations coupled with multi-phase moisture atmosphere

Abstract

The occurrence and development of cloud and precipitation are the products of the combination of atmospheric dynamic, thermal processes and cloud microphysical processes. In order to understand the interaction between these influencing factors in more detail, in this paper we study a moisture model with multi-phase for warm clouds, which consists of the primitive equations and a set of humidity equations where water is present in the form of water vapor, rain water and cloud condensates. This model has been considered by Cao et al. in (2018), where the velocity field is a given function in L∞((0,t1)×M). In this paper, the velocity field is governed by the atmosphere dynamic equation, which is more in line with the actual situation. In order to overcome the difficulty caused by the physical range requirement for the humidity, we introduce a new penalized function which is different from that introduced in Cao et al. (2018). Then we obtain the global existence of both quasi-strong solutions and strong solutions.