报告人：北京科技大学理学院陈艳萍教授

报告时间：2022.11.18星期五下午15：00-17：00

腾讯会议：734-421-165

报告题目：Some properties of generalized singular integrals related to the generalized dissipative QG equation

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.

个人简介：陈艳萍，北京科技大学数理学院副院长，教授，博士生导师。2007年博士毕业于北京师范大学。2009年获得全国优秀博士学位论文提名奖，2011年入选教育部“新世纪优秀人才支持计划”。主要研究方向为调和分析及其应用，并主持和参加多项国家自然科学基金。在Anal. &PDE、Trans. Amer. Math. Soc.、J. Funct. Anal.、Rev. Mat. Iberoam.等国内外知名杂志上发表学术论文多篇。