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Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes
Multi angle
Authors : Li, Jinkai (Author of the conference)
CIRM (Publisher )
35B45 - A priori estimates
35Q30 - Stokes and Navier-Stokes equations
35Q35 - PDEs in connection with fluid mechanics
76D03 - Existence, uniqueness, and regularity theory
76D09 - Viscous-inviscid interaction
35A01 - Existence problems: global existence, local existence, non-existence
35Q86 - PDEs in connection with geophysics
35D35 - Strong solutions
35M86 - Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
CIRM (Publisher )
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Abstract :
In this talk, I will present the global solvability of the primitive equations for the atmosphere coupled to moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. This moisture model, which has been used by Klein–Majda in [1] and corresponds to a basic form of the bulk microphysics closure in the spirit of Kessler [2] and Grabowski–Smolarkiewicz [3], contains closures for the phase changes condensation and evaporation, as well as the processes of autoconversion of cloud water into rainwater and the collection of cloud water by the falling rain droplets. The moisture balances are strongly coupled to the thermodynamic equation via the latent heat associated to the phase changes. The global well-posedness was proved by combining the technique used in Hittmeir–Klein–Li–Titi [4], where global well-posedness was established for the pure moisture system for given velocity, and the ideas of Cao–Titi [5], who succeeded in proving the global solvability of the primitive equations without coupling to the moisture.
Keywords : primitive equations; moisture dynamics; global well-posedness
MSC Codes : Keywords : primitive equations; moisture dynamics; global well-posedness
35B45 - A priori estimates
35Q30 - Stokes and Navier-Stokes equations
35Q35 - PDEs in connection with fluid mechanics
76D03 - Existence, uniqueness, and regularity theory
76D09 - Viscous-inviscid interaction
35A01 - Existence problems: global existence, local existence, non-existence
35Q86 - PDEs in connection with geophysics
35D35 - Strong solutions
35M86 - Nonlinear unilateral problems and nonlinear variational inequalities of mixed type
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 29/11/2019 Conference Date : 28/10/2019 Subseries : Research talks arXiv category : Analysis of PDEs Mathematical Area(s) : Analysis and its Applications ; PDE Format : MP4 (.mp4) - HD Video Time : 00:32:07 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-28_Li.mp4 
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Information on the Event
Event Title : Evolution Equations: Applied and Abstract Perspectives / Equations d'évolution: perspectives appliquées et abstraitesEvent Organizers : Disser, Karoline ; Haller-Dintelmann, Robert ; Kyed, Mads ; Saal, Jürgen Dates : 28/10/2019 - 01/11/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/2071.html
Citation Data
DOI : 10.24350/CIRM.V.19575603Cite this video as: Li, Jinkai (2019). Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19575603 URI : http://dx.doi.org/10.24350/CIRM.V.19575603 |
See Also
- [Multi angle] $L^p$-theory for Schrödinger systems / Author of the conference Rhandi, Abdelaziz.
- [Multi angle] Determining the global dynamics of the two-dimensional Navier-Stokes equations by a scalar ODE / Author of the conference Titi, Edriss S..
- [Post-edited] $L^{r}$-Helmholtz-Weyl decomposition in 3D exterior domains / Author of the conference Kozono, Hideo.
- [Multi angle] Dispersive decay for small localized solutions to the Korteweg-de Vries equation / Author of the conference Koch, Herbert.
Bibliography
- KLEIN, Rupert et MAJDA, Andrew J. Systematic multiscale models for deep convection on mesoscales. Theoretical and Computational Fluid Dynamics, 2006, vol. 20, no 5-6, p. 525-551. - https://doi.org/10.1007/s00162-006-0027-9
- KESSLER, Edwin. On the distribution and continuity of water substance in atmospheric circulations. In : On the distribution and continuity of water substance in atmospheric circulations. American Meteorological Society, Boston, MA, 1969. p. 1-84. - https://doi.org/10.1007/978-1-935704-36-2_1
- GRABOWSKI, Wojciech W. et SMOLARKIEWICZ, Piotr K. Two-time-level semi-Lagrangian modeling of precipitating clouds. Monthly Weather Review, 1996, vol. 124, no 3, p. 487-497. - https://doi.org/10.1175/1520-0493(1996)124<0487:TTLSLM>2.0.CO;2
- CAO, Chongsheng et TITI, Edriss S. Global well-posedness of the three-dimensional viscous primitive equations of large scale ocean and atmosphere dynamics. Annals of Mathematics, 2007, p. 245-267. - https://www.jstor.org/stable/20160059
- HITTMEIR, Sabine, KLEIN, Rupert, LI, Jinkai, et al. Global well-posedness for passively transported nonlinear moisture dynamics with phase changes. Nonlinearity, 2017, vol. 30, no 10, p. 3676. - https://arxiv.org/pdf/1610.00060.pdf
