Axi‐symmetrization near Point Vortex Solutions for the <scp>2D</scp> Euler Equation
Alexandru D. Ionescu, Hao Jia
Abstract
Abstract We prove asymptotic stability of point vortex solutions to the full Euler equation in two 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. © 2021 Wiley Periodicals LLC.
Topics & Concepts
Inviscid flowSymmetrizationVortexMathematicsEuler's formulaPerturbation (astronomy)Euler equationsMathematical analysisPoint (geometry)Classical mechanicsPhysicsGeometryMechanicsQuantum mechanicsNavier-Stokes equation solutionsComputational Fluid Dynamics and AerodynamicsFluid Dynamics and Turbulent Flows