时间：2022/05/25 10:00—12:00

腾讯会议：360-582-438

报告题目： Ill-posedness for the stationary Navier-Stokes equations in critical Besov spaces

报告摘要：In this talk, we will present some progress toward an open question which proposed by Tsurumi (Arch. Ration. Mech. Anal. 234:2, 2019): whether or not the stationary Navier-Stokes equations in $\R^d$ is well-posed from $\dot{B}_{p, q}^{-2}$ to $\mathbb{P} \dot{B}_{p, q}^{0}$ with $p=d$ and $1 \leq q < 2$. We demonstrate that for the case $1\leq q<2$ the 4D stationary Navier-Stokes equations is ill-posed from $\dot{B}_{4, q}^{-2}(\R^4)$ to $\mathbb{P} \dot{B}_{4, q}^{0}(\R^4)$ by showing that a sequence of external forces is constructed to show discontinuity of the solution map at zero. Indeed in such case of $q$, there exists a sequence of external forces which converges to zero in $\dot{B}_{4, q}^{-2}$ and yields a sequence of solutions which does not converge to zero in $\dot{B}_{4, q}^{0}$.

报告人简介：李金禄，赣南师范大学副教授，硕士生导师，主持在研（完成）国家自然科学基金青年项目及地区项目各一项、中国博士后科学基金特别资助（站中）项目及面上项目各一项、江西省自然科学基金青年项目一项，。在Advances in Mathematics, Journal of Functional Analysis, Journal of Differential Equations, Journal of Mathematical Fluid Mechanics等国外SCI刊物上发表论文30余篇。