English
Global well-posedness for the primitive equations coupled to nonlinear moisture dynamics with phase changes
Multi angle
Auteurs : Li, Jinkai (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 29/11/2019 Date de captation : 28/10/2019 Sous collection : Research talks arXiv category : Analysis of PDEs Domaine : Analysis and its Applications ; PDE Format : MP4 (.mp4) - HD Durée : 00:32:07 Audience : Researchers Download : https://videos.cirm-math.fr/2019-10-28_Li.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Evolution Equations: Applied and Abstract Perspectives / Equations d'évolution: perspectives appliquées et abstraitesOrganisateurs de la rencontre : Disser, Karoline ; Haller-Dintelmann, Robert ; Kyed, Mads ; Saal, Jürgen Dates : 28/10/2019 - 01/11/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2071.html
Données de citation
DOI : 10.24350/CIRM.V.19575603Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] $L^p$-theory for Schrödinger systems / Auteur de la Conférence Rhandi, Abdelaziz.
- [Multi angle] Determining the global dynamics of the two-dimensional Navier-Stokes equations by a scalar ODE / Auteur de la Conférence Titi, Edriss S..
- [ Post-edited] $L^{r}$-Helmholtz-Weyl decomposition in 3D exterior domains / Auteur de la Conférence Kozono, Hideo.
- [Multi angle] Dispersive decay for small localized solutions to the Korteweg-de Vries equation / Auteur de la Conférence Koch, Herbert.
Bibliographie
- 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
