报告题目: Non-uniqueness of weak solutions for the hypo-viscous compressible Navier-Stokes equations

报告人:   李亚纯 教授 （上海交通大学）

报告摘要：

We study the Cauchy problem for the isentropic hypo-viscous compressible Navier-Stokes equations under general pressure laws. By using convex integration method we provides the first non-uniqueness result of weak solutions to viscous compressible fluid. Due to the difficulties caused by the relative rigidity of the pressure and by the viscosity, our proof features new constructions of building blocks for both the density and momentum, which are, particularly, designed to respect the compressible structure. We provide first applications of a temporally intermittent but spatially homogeneous building block scheme and a mild density perturbation. It also applies to the compressible Euler equations and the hypo-viscous incompressible Navier-Stokes equations. This is a joint work with Peng Qu, Zirong Zeng, and Deng Zhang.

报告人简介：李亚纯，上海交通大学数学科学学院教授，博士生导师，长期从事非线性偏微分方程的理论及应用研究，发表论文80余篇，出版英文译著3本。主持了多项国家自然科学基金（含重点项目1项）和上海市自然科学基金项目，曾获上海市自然科学一等奖和上海市教学成果奖一等奖，入选教育部新世纪优秀人才支持计划，上海市曙光学者，国际期刊Communications on Pure & Applied Analysis和Commun. Math. Anal. Appl.编委。上海市工业与应用数学学会副理事长，教育部高等学校大学数学课程教学指导委员会委员。

报告时间: 2026.4.12(周日) 上午 10:30-11:30

报告地点: 逸夫楼1537