报告题目：Sharp non-uniqueness for the 2D hyper-dissipative Navier-Stokes equations

报告人：李心亮博士（深圳大学）

报告时间：5月7日（周三）下午15:30

报告地点：科技楼5075

报告摘要：In this article, we study the non-uniqueness of weak solutions for the two-dimensional hyper-dissipative Navier-Stokes equations in the super-critical spaces $L_{t}^{\gamma}W_{x}^{s,p}$ when the viscosity exponent $\alpha\in[1,\frac{3}{2})$, and obtain the conclusion that the non-uniqueness of the weak solutions at the two endpoints is sharp in view of the generalized Lady\v{z}enskaya-Prodi-Serrin condition with the triplet $(s,\gamma,p)=(s,\infty, \frac{2}{2\alpha-1+s})$ and $(s, \frac{2\alpha}{2\alpha-1+s}, \infty)$. By using the intermittency of the temporal concentrated function in an almost optimal way, we extend the recent elegant works on the non-uniqueness of 2D Navier-Stokes equations in [Cheskidov and Luo, Invent. Math., 229 (2022), pp. 987--1054; Cheskidov and Luo, Ann. PDE, 9:13 (2023)] to the hyper-dissipative case $\alpha \in(1,\frac{3}{2})$. In particularly, the viscosity exponent $\alpha=\frac{3}{2}$ is the upper limit for the one endpoint case $(s,\infty, \frac{2}{2\alpha-1+s})$ when $s=0$.

报告人简介：李心亮博士主要从事流体偏微分方程的数学理论研究，近年来对Navier-Stokes方程、无黏流体方程、MHD方程解的适定性和非适定性问题开展了一系列研究。特别是最近通过使用凸积分方法构造了2D超黏Navier-Stokes弱解的非唯一性结果、以及二维无黏Boussinesq方程的Onsager型猜想结果。已发表SCI论文10篇，相关成果发表在Nonlinearity、Commun. Contemp. Math.、J. Math. Anal. Appl.、Z. Angew. Math. Phys.、J. Math. Phys.、Acta Math. Sci. Ser. B (Engl. Ed.)等国内外学术期刊上。目前正在主持国家自然科学基金青年项目1项、中国博士后特别资助（站中）项目1项以及中国博士后面上资助项目1项。