A simple construction of the dynamical ${\Phi }_3^4$ model

Abstract

The ${\Phi }_3^4$ equation is a singular stochastic PDE with important applications in mathematical physics. Its solution usually requires advanced mathematical theories like regularity structures or paracontrolled distributions, and even local well-posedness is highly nontrivial. Here we propose a multiplicative transformation to reduce the periodic ${\Phi }_3^4$ equation to a well-posed random PDE. This leads to a simple and elementary proof of global well-posedness, which only relies on Schauder estimates, the maximum principle, and basic estimates for paraproducts, and in particular does not need regularity structures or paracontrolled distributions.

References in corpus (3)

• Multidimensional SDE with distributional drift and Lévy noise
• A priori bounds for the ${\Phi }^4$ equation in the full sub-critical regime
• The ${\Phi }_3^4$ measure has sub-Gaussian tails

Cited by in corpus (1)

• Finite speed of propagation for the 2- and 3-dimensional multiplicative stochastic wave equation