Instability of the 2D Taylor-Green vortex
数学专题报告
报告题目(Title)：Instability of the 2D Taylor-Green vortex
报告人(Speaker)：Michele Dolce (École Polytechnique Fédérale de Lausanne)
地点(Place)：Zoom ID: 872 819 32131 | Password: 123456
时间(Time)：2026年6月10日（周三）16:00-17:00
邀请人(Inviter)：薛留堂
报告摘要
The 2D Taylor-Green (TG) vortex is the prototypical example of an Euler steady state on T^2 possessing truly two-dimensional features, like elliptic and hyperbolic stagnation points. Its stream function, sin(x)sin(y), lives on the second Fourier shell, making it susceptible to large-scale destabilizing mechanisms. Despite the apparent simplicity of the steady state, a proof of its spectral instability has long remained elusive, and was only recently observed numerically. To solve this problem, I will introduce a new criterion to detect unstable eigenvalues for a wide class of linear Hamiltonian operators. We apply this to prove the stability of the TG vortex with respect to odd perturbations. In the subspace of functions even in both variables, we combine our criterion with a rigorous computer-assisted argument to locate two unstable eigenvalues. This fully characterizes the unstable spectrum of the TG vortex and implies nonlinear instability in velocity. This is a joint work with G. Cao-Labora, M. Colombo and P. Ventura.
