Speaker: 牛冬娟 教授，首都师范大学
Inviter: 韩丕功 研究员
Title: Analysis aspect of tropical climate models
Time & Venue: 2025.12.10 10:00-11:00 腾讯会议 184-803-734
Abstract: In this talk, I will primarily present the mathematical theory of TCM, which includes its well-posedness, large-time behavior, and nonlinear stability around the shear flows. Precisely, I first introduce the global well-posedness and large-time behavior of 2D TCM under smallness assumption of the initial data. To explore the intrinsic relationship between the first baroclinic mode of the velocity and temperature, we further investigate the stability around the steady-state solution and the optimal time decay rates for 3D TCM. The key points here are that we remove the smallness assumption on the lower-frequency part of the initial data and establish both the upper and lower bounds of the time decay rate. Finally, we prove the nonlinear stability around the Couette flow for 2D viscous TCM by virtue of the enhanced dissipation generated by the non-self-adjoint operator y\partial_x-\Delta.
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