数学学院基础数学学术报告
--- 分析、偏微分方程与动力系统讨论班(2024春季第15讲)
Characterization of logarithmic $Q$ spaces with application to regularity of fractional Nasiver-Stokes equations
李澎涛(青岛大学)
时间:2024年06月17日(周一)下午16:00-17:00
地点:沙河国实 E706
摘要: We study the regularity of fractional Navier-Stokes equations with data in logarithmic $Q$ spaces $Q^{-1}_{l,k,\beta}(\mathbb R^{n})$. Compared with the classical $Q$ type spaces, the existence of the logarithmic functions makes it difficult to characterize $Q^{-1}_{l,k,\beta} (\mathbb R^{n})$ via the high-order derivatives of fractional heat semigroups. Applying the regular wavelets, we introduce a new method which is independent of the theories of Hausdorff capacities and predual spaces to establish the Carleson measure characterizations of $Q^{-1}_{l,k,\beta}(\mathbb R^{n})$. Then, the regularity estimates of the solutions to fr ac tio nal Navier-Stokes equations are obtained.
报告人简介: 李澎涛,男,青岛大学数学与统计学院教授。主要从事的研究方向包括调和分析、小波分析、偏微分方程等。2009年博士毕业于北京大学十大网投靠谱网站基础数学专业。主持包括国家自然科学基金面上项目、山东省优秀青年基金等各类科研项目7项。作为第一作者或通讯作者在Cal.Var.PDE.,J. Funct. Anal.等重要学术刊物上发表论文70 余篇,出版专著1部。欢迎大家参加!