Global well-posedness of the dynamic $\Phi^4$ model in the plane

TL;DR

This paper proves the global well-posedness of the dynamic ^4 model, a nonlinear stochastic PDE, in the plane, using renormalization and weighted Besov spaces of negative regularity.

Contribution

It establishes the first global well-posedness result for the dynamic ^4 model in two dimensions with solutions in weighted Besov spaces.

Findings

Solutions exist globally in time

The model requires renormalization for well-posedness

Solutions are in weighted Besov spaces of negative regularity

Abstract

We show global well-posedness of the dynamic $\Phi^4$ model in the plane. The model is a non-linear stochastic PDE that can only be interpreted in a "renormalised" sense. Solutions take values in suitable weighted Besov spaces of negative regularity.