2019/04/19 by Alexandru D. Ionescu, Hao Jia, Ionescu, Alexandru +1 · 4 citations
Mathematics · Engineering · #Navier-Stokes equation solutions #Fluid Dynamics and Turbulent Flows #Computational Fluid Dynamics and Aerodynamics
paper · pdf · doi:10.48550/arxiv.1904.09170
We prove a definitive theorem on the asymptotic stability of point vortex solutions to the full Euler equation in 2 dimensions. More precisely, we show that a small, Gevrey smooth, and compactly supported perturbation of a point vortex leads to a global solution of the Euler equation in 2D, which converges weakly as t→∞ to a radial profile with respect to the vortex. The position of the point vortex, which is time dependent, stabilizes rapidly and becomes the center of the final, radial profile. The mechanism that leads to stabilization is mixing and inviscid damping.