报告题目 (Title)：关于耗散QG方程的广义奇异积分的性质

报告人 (Speaker)：陈艳萍 教授（北京科技大学）

报告时间 (Time)：2022年1月13日(周四) 9:00

报告地点 (Place)：线上腾讯会议，会议 ID：291-255-332

邀请人(Inviter)：赵发友

主办部门：理学院 数学系

报告摘要：This talk is concerned with a kind of singular integrals T_\beta which can be viewed as an extension of the classical Calder\'{o}n-Zygmund type singular integral. This kind of singular integrals appears in the the generalized 2D dissipative quasi-geostrophic (QG) equation. First, we give a relationship between T_\beta and a Calder\'{o}n-Zygmund singular integral operator for \beta\in [0,n). Moreover, we give an uniform sparse domination for the generalized singular integral operators T_\beta for \beta\in [0, n). Finally, we study solutions to the generalized 2D dissipative quasi-geostrophic (QG) equation. We prove existence of global weak solutions, weak solutions also exist globally but are proven to be unique only in the class of strong solutions and obtain the detailed aspects of large time approximation.