Global regularity of axisymmetric Euler equations without swirl in higher dimensions 

Speaker: 邵锋 博士，北京大学数学科学学院

Inviter: 秦国林

Title: Global regularity of axisymmetric Euler equations without swirl in higher dimensions 

Time & Venue: 2025.8.27  10:30-11:30  南楼212

Abstract: We consider the axisymmetric incompressible Euler equations without swirl in $\mathbb R^d$ or in a cylinder domain for $d\geq3$. For $3\leq d\leq 6$, we prove the global regularity under the following conditions: $u_0\in L^2(\mathbb R^d)$, $\omega_0/r^{d-2}\in L^{\frac{d}{d-2},\infty}(\mathbb R^d)$ and $\min\{1, r^{3-d}\}\omega_0/r^\alpha\in L^\infty(\mathbb R^d)$ for some $\alpha\in(0,1)$. Moreover, if the domain is a cylinder or if  $\omega_0$ is single-signed, we prove the same global regularity result for all $d\geq3$. Additionally, for $3\leq d\leq 6$, we obtain the same growth bounds as in [Lim and Jeong, Arch. Ration. Mech. Anal., 249, Paper No. 32 (2025)], without assuming compact support on the initial data. This talk is based on a joint work with Dongyi Wei and Zhifei Zhang.