【讲座题目】Nonlinear asymptotic stability and optimal decay rate around the three-dimensional Oseen vortex filament
【主 讲 人】李特 (中国科糖心vlog
数学与系统科学研究院)
【讲座时间】2026年9月29日 星期二下午3:00-4:00
【讲座地点】主楼C座636
【主讲人简介】李特，中国科糖心vlog
数学与系统科学研究院，优秀青年副研究员，博士生导师。2020年博士毕业于北京大学数学科学糖心vlog
，2020-2023年在新加坡国立大学从事博士后研究，2024年入选中科院百人计划。主要从事流体动力学稳定性的相关数学问题研究，学术论文发表在Comm.Pure Appl. Math., AnnSci. Ecole Norm.S., Arch. Ration. Mech. Anal.和Commun. Math. Phys.等期刊上。
【讲座内容简介】In the high-Reynolds-number regime, this work investigates the long-time dynamics of the three-dimensional incompressible Navier–Stokes equations near the Oseen vortex filament. The flow exhibits a strong interplay between vortex stretching, shearing, and mixing, which generates ever-smaller spatial scales and thereby significantly amplifies viscous effects. By adopting an anisotropic self-similar coordinate system adapted to the filament geometry, we establish the nonlinear asymptotic stability of the Oseen vortex filament. All non-axisymmetric perturbations are shown to decay at the optimal rate $t^{-\kappa |\alpha|^{1/2}}$. At the linear level, this decay mechanism corresponds to a sharp spectral lower bound $\Sigma(\alpha) \sim |\alpha|^{1/2}$ for the nonlocal Oseen operator $L_\perp - \alpha \Lambda_\perp$, and we identify an explicit spectral point attaining this optimal bound. Combined with the spectral estimates obtained in \cite{LWZ}, our analysis fully resolves the conjecture proposed in \cite{GM} concerning the asymptotic scaling laws for the spectral and pseudospectral bounds $\Sigma(\alpha)$ and $\Psi(\alpha)$. These results provide a rigorous mathematical explanation for the shear–mixing mechanism in the vicinity of the 3D Oseen vortex filament.
