Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole. (June 2022)

• Record Type: Journal Article
• Authors: Choi, Kyudong; Jeong, In-Jee
• Is Part Of: Nonlinear analysis. Volume 65(2022)
• Publication Date: 2022-06
• Subjects: 2D Euler equation -- Lamb dipole -- Stability -- Gradient growth -- Large time behavior -- Particle trajectory; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2021.103470
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We prove linear in time filamentation for perturbations of the Lamb dipole, which is a traveling wave solution to the incompressible Euler equations in R 2 . The main ingredient is a recent nonlinear orbital stability result by Abe–Choi. As a consequence, we obtain linear in time growth for the vorticity gradient for all times, for certain smooth and compactly supported initial vorticity in R 2 . The construction carries over to some generalized SQG equations.