Existence of concentrated multiscale vortex solutions for 2D Euler and clustered helical solutions for 3D Euler equations

Speaker: 万捷 副教授, 北京理工大学数学与统计学院

Inviter: 秦国林

Title: Existence of concentrated multiscale vortex solutions for 2D Euler and clustered helical solutions for 3D Euler equations 

Language: Chinese

Time & Venue: 2025.7.9 15:20-16:20  南楼205

Abstract: In this talk, I will focus on the vortex desingularization problem of 2D/3D incompressible Euler equations. For 2D Euler equation, we show the existence of multiscale-bump vortex solutions with different profiles in bounded domains by the vorticity method. For 3D Euler equation, we prove the existence of certain clustered helical vortex solutions in helical domains by finite-dimensional reduction method. Especially, we show the relation between this kind of solutions and the so called “nearly paralleled vortex filament” model derived by Klein-Majda-Damodaran. This is a joint work with Prof. Cao.