# Regularization by noise for the point vortex model of mSQG equations

## TL;DR

This paper demonstrates that adding specific space-dependent noise to the point vortex model of mSQG equations ensures global well-posedness for all initial conditions, preventing vortex collapse observed in the deterministic case.

## Contribution

It introduces a noise regularization technique that guarantees unique global solutions for the point vortex model of mSQG equations, extending well-posedness results.

## Key findings

- Noise induces global solutions for all initial conditions.
- Deterministic system can have vortex collapse.
- Explicit example of vortex collapse in deterministic case.

## Abstract

We consider the point vortex model corresponding to the modified Surface Quasi-Geostrophic (mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditions. We show that, when the system is perturbed by a certain space-dependent noise, it admits a unique global solution for any initial configuration. We also present an explicit example for the deterministic system where three different point vortices collapse.