06-12-2017
186

数学系讲座:Some mathematical analyses on dynamical models for atmosphere with moisture

演讲人:李进开

讲座时间:2017-12-07 15:00:00

讲座地点:环境学院楼316

讲座内容

In this talk, we will present some recent mathematical results, mainly the global wellposedness and convergence of the relaxation limit, on two kinds of dynamical models for the atmosphere with moisture. In the rst part of this talk, which is a joint work with Edriss S. Titi [1], we will consider a tropical atmosphere model introduced by Frierson, Majda, and Pauluis (Commum. Math. Sci. 2004); for this model, we will present the global well-posedness of strong solutions and the strong convergence of the relaxation limit, as the relaxation time " tends to zero. It will be shown that, for both the nitetime and instantaneous-relaxation systems, the H1 regularities on the initial data are sucient for both the global existence and uniqueness of strong solutions, but slightly more regularities than H1 are required for both the continuous dependence and strong convergence of the relaxation limit. In the second part of this talk, which is a joint work with Sabine Hittmeir, Rupert Klein, and Edriss S. Titi [2], we will consider a moisture model for warm clouds used by Klein and Majda (Theor. Comput. Fluid Dyn. 2006), where the phase changes are allowed, and we will present the global well-posedness of this system.

[1] Jinkai Li; Edriss S. Titi: A tropical atmosphere model with moisture: global well-posedness and relaxation limit, Nonlinearity, 29 (2016), 2674-2714.

[2] Sabine Hittmeir; Rupert Klein; Jinkai Li; Edriss S. Titi: Global well-posedness for passively transported nonlinear moisture dynamics with phase changes, Nonlinearity 30 (2017) 3676-C3718.

演讲人简介

李进开,香港中文大学

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