On the onset of filamentation on two-dimensional vorticity interfaces

TL;DR

This paper investigates the formation of filaments on 2D vorticity interfaces using an asymptotic nonlinear model, revealing structural properties, and establishing the existence of global weak solutions and traveling waves.

Contribution

It introduces a new asymptotic nonlinear model for filamentation, analyzes its structure, and proves the existence of global weak solutions and traveling wave solutions.

Findings

Structural properties of the model are identified.

Global weak solutions are constructed.

Existence of traveling wave solutions is proven.

Abstract

We study an asymptotic nonlinear model for filamention on two-dimensional vorticity interfaces. Different re-formulations of the model equation reveal its underlying structural properties. They enable us to construct global weak solutions and to prove the existence of traveling waves.