报告题目：Stochastic Navier-Stokes equation II: Harmonic and stochastic analysis tools

报 告 人：王玉昭 教授 英国伯明翰大学

报告时间：2025年5月16日，19：00-20：30

报告链接：Join Zoom Meeting ID: 856 3669 3919

//bham-ac-uk.zoom.us/j/85636693919?pwd=KWBEyFBSGw13jndDvXFMG3aQTsaLJc.1

校内联系人：段犇 [email protected]

报告摘要：

In this lecture, we continue our series on the stochastic Navier-Stokes equations driven by additive white noise. So far, we have addressed the well-posedness of the 2D deterministic Navier-Stokes equations on the torus, as well as the stochastic counterpart by assuming some key estimates from harmonic and stochastic analysis. Specifically, we relied on: Harmonic analysis tools (e.g., Fourier analysis, Bony decomposition, Besov spaces, and Schauder estimates), and stochastic techniques (e.g., Wiener chaos expansion and hypercontractivity) to handle the noise term. In this lecture, we will revisit these tools, which are fundamental to the study of stochastic PDEs.

References:

• Da Prato, G.; Debussche, A. Two-dimensional Navier-Stokes equations driven by a space-time white noise. J. Funct. Anal. 196 (2002), no. 1, 180–210.

• Bahouri, H.; Chemin, J.-Y.; Danchin, R. Fourier analysis and nonlinear partial differential equations. Grundlehren Math. Wiss., 343, Springer, Heidelberg (2011).

• Simon, B.: The P (ϕ)2 Euclidean (quantum) Field Theory, Princeton Series in Physics. Princeton University Press, Princeton (1974).

• Hui-Hsiung Kuo, Introduction to Stochastic Integration, Universitext Springer, New York, 2006, xiv+278 pp.

报告人简介：王玉昭，英国伯明翰大学教授，博士生导师。 2005年获吉林大学数学与应用数学学士学位，2010年获北京大学数学博士学位。自2017年8月起在英国伯明翰大学任助理教授，副教授。王玉昭教授主要从事于无穷维动力系统，随机偏微分方程，调和分析的研究 —— 集中于无穷维动力系统的不变测度，随机波动方程的整体适定性相关问题。