学术报告

题      目：Stability and large-time behavior of 2D tropical climate model with zero thermal dissipation

报  告  人：牛冬娟  教授  (邀请人：丁时进 )

                                    首都师范大学

时      间：10月14日  09：00-10：00

地     点：数科院西楼111报告厅

报告人简介:

        牛冬娟，首都师范大学数学科学学院教授，博士生导师。主要研究不可压缩Navier-Stokes方程及相关流体模型解的适定性及渐近行为以及边界层问题等。曾多次受邀访问美国、香港、巴西、波兰等知名学府及科研机构并多次在国际重要学术会议上做邀请报告。在国际知名期刊SIAM Journal on Mathematical Analysis、Indiana Univ. Math. J.等发表20余篇学术论文。多次获得国家自然科学基金及北京市自然科学基金资助。

摘      要：

       In this talk, we are concerned with stability problem and large-time behavior of 2D tropical climate model with zero thermal dissipation under small initial data.  The first one studys the global well-posedness and large time behavior of solutions of the system with $-\Delta u$ and a damping term $v$ in the whole space. The key ingredient here is the explicit large-time decay rate of solutions. The second one studys that stability of Couette flow to the system with $-\Delta u$, $-\Delta v$ and a damping term $v$ in the domain $\mathbb{T}\times \mathbb{R} $. The key is fully utilizing the enhanced dissipation created by the operator $y\partial_{x}-\nu\Delta$ and construction of the Fourier operator $\mathcal{M}$. It is emphasized that the absences of thermal dissipation and ${\rm div}v=0$ cause great difficulties to solve the stability problem. By exploiting the structure of the system, we establish the expected stability results. These are joint works with doctoral student Wu Huiru.

     

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