# The inviscid limit of Navier-Stokes equations for vortex-wave data on $\mathbb{R}^2$

## TL;DR

This paper proves that solutions of the Navier-Stokes equations on the plane with vortex-wave initial data converge to the vortex-wave system as viscosity vanishes, rigorously justifying this model from physical flows.

## Contribution

It provides a rigorous mathematical proof of the inviscid limit for vortex-wave initial data, connecting Navier-Stokes solutions to the vortex-wave system.

## Key findings

- Convergence of Navier-Stokes solutions to vortex-wave system as viscosity approaches zero.
- Validation of the vortex-wave model as a limit of physical Navier-Stokes flows.
- Extension of previous vortex-point analysis to include regular vorticity components.

## Abstract

We establish the inviscid limit of the incompressible Navier-Stokes equations on the whole plane $\mathbb{R}^2$ for initial data having vorticity as a superposition of point vortices and a regular component. In particular, this rigorously justifies the vortex-wave system from the physical Navier-Stokes flows in the vanishing viscosity limit, a model that was introduced by Marchioro and Pulvirenti in the early 90s to describe the dynamics of point vortices in a regular ambient vorticity background. The proof rests on the previous analysis of Gallay in his derivation of the vortex-point system.