Global regularity and large time behavior of the 2D SQG equation with anisotropic fractional dissipation
报告题目(Title)：Global regularity and large time behavior of the 2D SQG equation with anisotropic fractional dissipation
报告人(Speaker)： 叶专 副教授 江苏师范大学
地点(Place)：腾讯会议 ID：382 272 598
时间(Time)：2021-07-15（星期四）， 3:00-4:00 pm （Beijing Time）
邀请人(Inviter)：许孝精, 袁迪凡
报告摘要
In this talk, we focus on the two-dimensional surface
quasi-geostrophic equation with fractional horizontal dissipation and fractional vertical thermal diffusion. On the one hand, when the dissipation powers are restricted to a suitable range, the global regularity of the surface quasi-geostrophic equation is obtained by some anisotropic embedding and interpolation inequalities involving fractional derivatives, which can be regarded as an alternative approach to the global regularity result derived in our previous work (Nonlinearity 2020)
and plays a critical role in deriving the decay estimates of the solutions. One the one hand, we obtain the optimal large time decay estimates for global weak solutions by an anisotropic interpolation inequality. Furthermore, based on the argument adopted in establishing the global $\dot{H}^1$-norm of the solution, we obtain the optimal large time decay estimates for the above obtained global smooth solutions. Finally, the decay estimates for the difference between the full solution and the solution to the corresponding linear part are also derived.
主讲人简介
叶专，2016年6月获得北京师范大学理学博士学位。毕业至今任职于江苏师范大学，现任副教授，硕士生导师，主要从事流体动力学方程的适定性问题。主持过1项国家青年科学基金和 1项江苏省青年科学基金。入选2020年度江苏省“青蓝工程”优秀青年骨干教师，部分论文发表在国际重要期刊J. Math. Pures Appl.，Nonlinearity，J. Differential Equations，J. Nonlinear Science，DCDS-A， Pacific J. Math.
