Traveling vortex pairs for 2D incompressible Euler equations

TL;DR

This paper constructs steady vortex pairs for 2D incompressible Euler equations, providing a desingularization of point vortices using an improved vorticity method, advancing understanding of vortex dynamics.

Contribution

It introduces a new family of steady vortex pairs with general vorticity, extending the desingularization of point vortices in 2D Euler flows.

Findings

Constructed steady vortex pairs with general vorticity functions.

Achieved desingularization of point vortices with equal and opposite strengths.

Utilized an improved vorticity method for the construction.

Abstract

In this paper, we study desingularization of vortices for the two-dimensional incompressible Euler equations in the full plane. We construct a family of steady vortex pairs for the Euler equations with a general vorticity function, which constitutes a desingularization of a pair of point vortices with equal magnitude and opposite signs. The results are obtained by using an improved vorticity method.