Speaker：Dr. Xiaoxin Zheng, Beihang University

Title: The 2D Euler equation in Yudovich and bmo-type Spaces

Time：2019-06-11, 15:30-16:30

Venue：Room 316 of Environment Building, Rennin University

Abstract： We construct global-in-time, unique solutions of the two-dimensional Euler equations in a Yudovich type space and a bmo-type space. First, we show the regularity of solutions for the two-dimensional Euler equations in the Spanne space involving an unbounded and non-decaying vorticity. Next, we establish an estimate with a logarithmic loss of regularity for the transport equation in a bmo-type space by developing classical analysis tool such as the John–Nirenberg inequality. We also optimize estimates of solutions to the vorticity-stream formulation of the two-dimensional Euler equations with a bi-Lipschitz vector field in bmo-type space by combining an observation introduced by Yodovich with the so-called “quasi-conformal property” of the incompressible flow.

演讲人简介：

郑孝信(xiaoxinzheng@buaa.edu.cn)，研究领域为调和分析、流体动力学方程等非线性偏微分方程的数学理论。已在ARMA, CMP, JMPA, Rev. Mat. Iberoam., SIMA,  JDE,  Nonlinearity等杂志上发表二十余篇学术论文；研究得到国家自然科学基金青年基金与面上项目的资助。