报告题目：Global Kato's solutions for inhomogeneous Navier-Stokes System in L³(R³)

报告人：吕沛博士（香港中文大学）

主持人：吴成发副教授

报告时间：2024年11月12日周二16：30-17：30

报告地点：致知楼207

报告摘要：

Due to the low regularity of solutions, global-in-time solutions in the sense of Kato for the inhomogeneous incompressible Navier-Stokes equations are remarkably challenging even when the initial density is a small fluctuation of a positive constant. This problem is successfully addressed under the condition that $\left\|v_{0}\right\|_{\dot{H}^{\frac{1}{2}} (\mathbb{R}^{3})}$ is bounded, but not necessarily small. The key strategy involves the partial regularity for incompressible Navier-Stokes equations, a refined estimate of pressure, and a covering argument.

报告人简介：

His research interests are the partial regularity of nonlinear partial differential equations and the well-posedness of nonlinear partial differential equations with initial values in parabolic scaling invariant function spaces. He got a bachelor's degree in mathematics from Shenzhen University in 2020. He obtained his Ph.D. in Mathematics from the City University of Hong Kong in 2024 and now holds a postdoctoral position at the Chinese University of Hong Kong.

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