# Motion of a Vortex Filament in an External Flow

## TL;DR

This paper models the motion of a vortex filament in an external flow using a nonlinear equation, proving local existence and uniqueness of solutions for a closed filament in an incompressible, inviscid fluid.

## Contribution

It introduces a nonlinear model incorporating external flow effects and establishes local well-posedness for the vortex filament problem.

## Key findings

- Proves unique local solvability of the vortex filament equation.
- Models the filament motion with external flow effects.
- Provides mathematical foundation for vortex filament dynamics in external flows.

## Abstract

We consider a nonlinear model equation describing the motion of a vortex filament immersed in an incompressible and inviscid fluid. In the present problem setting, we also take into account the effect of external flow. We prove the unique solvability, locally in time, of an initial value problem posed on the one dimensional torus. The problem describes the motion of a closed vortex filament.