Mathematical Analysis of Atmospheric and Oceanic Dynamics Models: Cloud Formation and Sea-ice Models
In this talk we will present rigorous analytical results concerning global regularity, in the viscous case, and finite-time singularity, in the inviscid case, for oceanic and atmospheric dynamics models. Moreover, we will also provide a rigorous justification of the derivation of the Primitive Equations of planetary scale oceanic dynamics from the three-dimensional Navier-Stokes equations as the vanishing limit of the small aspect ratio of the depth to horizontal width.
Overview
Abstract
Coffee Time : 15:30 to 16:00
In this talk we will present rigorous analytical results concerning global regularity, in the viscous case, and finite-time singularity, in the inviscid case, for oceanic and atmospheric dynamics models. Moreover, we will also provide a rigorous justification of the derivation of the Primitive Equations of planetary scale oceanic dynamics from the three-dimensional Navier-Stokes equations as the vanishing limit of the small aspect ratio of the depth to horizontal width. In addition, we will also show the global well-posedeness of the coupled three-dimensional viscous Primitive Equations with a micro-physics phase change moisture model for cloud formation. Eventually, we will also present short-time well-posedness of solutions to the Hibler's sea-ice model.
Brief Biography
Edriss S. Titi received his doctorate in 1986 under the supervision of Ciprian Foias. Currently, he holds the Nonlinear Mathematical Sciences Professorial Chair at the University of Cambridge, UK; is a University Distinguished Professor and the Arthur Owen Professor of Mathematics in Texas A&M University.
Titi’s research in applied and computational mathematics lies at the interface between rigorous applied analysis and physical applications. Specifically, in studying the Euler and the Navier-Stokes and other related nonlinear partial differential equations. The applications include, fluid mechanics, oceanic and atmospheric dynamics and their coupling with moisture micro-physics in clouds formation, turbulence, chemical reactions, nonlinear fiber optics, control theory and data assimilation for weather and climate prediction.
Titi is a Fellow of the American Mathematical Society, the Society of Industrial and Applied Mathematics, the John Simon Guggenheim Memorial Foundation, USA; and the Institute of Physics, UK. He is the recipient of many international scientific awards including the Stanislaw M. Ulam Distinguished Scholar, the Humboldt Research Award for Senior U.S. Scientists, Germany, the Einstein Visiting Fellow, Germany and the Gaspard Monge Distinguished Professorship, France. He is also a co-recipient of the Society for Industrial and Applied Mathematics (SIAM) Prize on Best Paper in Partial Differential Equations (2009), and the 2020 International Consortium of Chinese Mathematicians Best Paper Award (Gold Medal).
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