# Global well-posedness of complex Ginzburg-Landau equation with a space-time white noise

## TL;DR

This paper establishes the global well-posedness of the complex Ginzburg-Landau equation driven by space-time white noise on a 3D torus, extending stochastic PDE theory with novel a priori estimates.

## Contribution

It introduces a new approach to prove global existence for stochastic CGL equations using paracontrolled calculus, inspired by methods from the dynamical $\

## Key findings

- Proves global well-posedness of stochastic CGL on 3D torus.
- Develops a priori $L^{2p}$ estimates for solutions.
- Extends techniques from stochastic $\

## Abstract

We show the global-in-time well-posedness of the complex Ginzburg-Landau (CGL) equation with a space-time white noise on the 3-dimensional torus. Our method is based on [14], where Mourrat and Weber showed the global well-posedness for the dynamical $\Phi_3^4$ model. We prove a priori $L^{2p}$ estimate for the paracontrolled solution as in the deterministic case [5].