Global Well-Posedness of 2D Euler-$\alpha$ Equations in Exterior Domain

TL;DR

This paper proves the global existence and uniqueness of solutions for 2D Euler-$ extalpha$ equations in exterior domains by deriving key estimates from vorticity-stream function formulations.

Contribution

It establishes the first rigorous proof of global well-posedness for Euler-$ extalpha$ equations in exterior domains using vorticity estimates.

Findings

Global existence and uniqueness of solutions in exterior domains

Key estimates derived from vorticity-stream function formulation

Conditions on initial data regularity

Abstract

After casting Euler-$\alpha$ equations into vorticity-stream function formula, we obtain some very useful estimates from the properties of the vorticity formula in exterior domain. Basing on these estimates, one can have got the global existence and uniqueness of the solutions to Euler-$\alpha$ equations in 2D exterior domain provided that the initial data is regular enough.