Concentrating solutions for a Liouville type equation with variable intensities in 2D-turbulence

TL;DR

This paper constructs sign-changing concentrating solutions for a mean field equation modeling turbulent Euler flows with variable vortex intensities and orientations, analyzing their impact on vortex configurations.

Contribution

It introduces a method to construct sign-changing solutions for a Liouville type equation with variable vortex intensities and orientations, advancing understanding of 2D turbulence models.

Findings

Effect of variable intensities on bubbling profiles

Influence of vortex orientation on vortex point locations

Construction of sign-changing solutions in turbulent flow models

Abstract

We construct sign-changing concentrating solutions for a mean field equation describing turbulent Euler flows with variable vortex intensities and arbitrary orientation. We study the effect of variable intensities and orientation on the bubbling profile and on the location of the vortex points.