Global Well-Posedness for the Thermodynamically Refined Passively Transported Nonlinear Moisture Dynamics with Phase Changes
In this work we study the global solvability of moisture dynamics with phase changes for warm clouds. We thereby in comparison to previous studies (Hittmeir et al. in Nonlinearity 30:3676–3718, 2017) take into account the different gas constants for dry air and water vapor as well as the different heat capacities for dry air, water vapor and liquid water, which leads to a much stronger coupling of the moisture balances and the thermodynamic equation. This refined thermodynamic setting has been demonstrated to be essential, e.g. in the case of deep convective cloud columns in Hittmeir and Klein (Theoret Comput Fluid Dyn 32(2):137–164, 2017). The more complicated structure requires careful derivations of sufficient a priori estimates for proving global existence and uniqueness of solutions.
Acknowledgements: S.H. acknowledges support by the Austrian Science Fund via the previous Hertha-Firnberg project T-764 and via the SFB “Taming Complexity in Partial Differential Systems” with project number F 65. R.K. acknowledges support by Deutsche Forschungsgemeinschaft through Grant CRC 1114 “Scaling Cascades in Complex Systems”, projects A02 and C06. J.L. acknowledges support by the National Natural Science Foundation of China (11971009 and 11871005), by the Guangdong Basic and Applied Basic Research Foundation (2019A1515011621, 2020B1515310005, 2020B1515310002, and 2021A1515010247), and by the Key Project of National Natural Science Foundation of China (12131010). E.S.T. acknowledges support by the Einstein Stiftung/Foundation-Berlin, Einstein Visiting Fellowship No. EVF-2017-358. RK thanks the Centre International de Rencontres Mathématique (CIRM) and the city of Marseille for their support in the framework of their Jean Morlet Chair programme on “Nonlinear partial differential equations in fluid mechanics". RK and EST would also like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme TUR when part of this work was undertaken. This work was supported by EPSRC Grant Number EP/R014604/1.