数学科学学院学术报告[2025]2号

(高水平大学建设系列报告1025号)

报告题目: Double H\"{o}lder regularity of the hydrodynamic pressure for weak solutions of Euler equations

报告人：李思然 副教授（上海交通大学）

报告时间：2025年1月8日10:30-11:30

讲座地点：深圳大学粤海校区汇星楼514

报告内容：We give an elementary proof for the double H\"{o}lder regularity of the hydrodynamic pressure for weak solutions of the Euler Equations in a bounded $C^2$-domain $\Omega \subset \R^d$; $d\geq 3$. That is, for velocity $u \in C^{0,\gamma}(\Omega;\R^d)$ with some $0<\gamma<1/2$, we show that the pressure $p \in C^{0,2\gamma}(\Omega)$. This regularity result has recently been established in [L. De Rosa, M. Latocca, and G. Stefani, Int. Math. Res. Not. 2024.3 (2024), 2511--2560] over $C^{2,\alpha}$-domains by means of pseudodifferential calculus. In contrast, our approach involves only standard elliptic PDE techniques, and relies on a variant of the modified pressure introduced in [C. W. Bardos, D. W. Boutros, and E. S. Titi, H\"{o}lder 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of the 3D Euler equations in bounded domains, arXiv: 2304.01952] and the potential estimates in [L. Silvestre, online unpublished notes].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 $\partial\Omega$. Our arguments also yield delicate quantitative estimates up to the boundary uncovered by the aforementioned work of De Rosa--Latocca--Stefani. **Joint work with Ya-Guang Wang*

报告人简历：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，导师为陈贵强教授。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副教授。主要从事偏微分方程方向的研究，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。

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邀请人：李心亮

数学科学学院

2024年12月30日