报告题目：Double  regularity of the hydrodynamic pressure for weak solutions of Euler equations

报告简介：We give an elementary proof for the double  regularity of the hydrodynamic pressure for weak solutions of the Euler Equations in a bounded  ; . That is, for velocity  with some , we show that the pressure . This is motivated by the studies of turbulence and anomalous dissipation in mathematical hydrodynamics and, recently, has been  established in [L. De Rosa, M. Latocca, and G. Stefani, Int. Math. Res. Not.  2024.3 (2024), 2511--2560] over  by means of pseudodifferential calculus. Our approach involves only standard elliptic PDE techniques, and relies crucially on a variant of the modified pressure introduced in [C. W. Bardos, D. W. Boutros, and E. S. Titi,  regularity of the pressure for weak solutions of the 3D Euler equations in bounded domains, arXiv: 2304.01952] and the potential estimates in [L. Silvestre, unpublished notes]. The key novel ingredient of our proof is the introduction of two cutoff functions whose localisation parameters are carefully chosen as a power of the distance to .

*Joint work with Prof. Ya-Guang Wang. 

报告人：李思然 上海交通大学

个人简介：李思然，上海交通大学副教授。2017年从英国牛津大学获得博士学位，导师为陈桂强教授。2017-2019年在美国莱斯大学进行博士后研究，合作导师为Robert Hardt教授。2020-2021年在上海纽约大学任访问助理教授。2021年9月起任上海交通大学长聘教轨副教授。2024年入选中国科协第九届青年人才托举工程项目。主要从事偏微分方程的研究，特别关注来源于流体力学及微分几何问题的偏微分方程。目前已在Arch. Ration. Mech. Anal.、J. Funct. Anal.、J. Math. Pures Appl. 等国际国内知名期刊上发表论文二十余篇。

报告时间：2025年2月28日 上午9:00-11:30

报告地点：扬州大学瘦西湖校区56号楼数学科学学院208会议室

主办单位：扬州大学数学科学学院

联系人：唐童

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