Renormalized powers of Ornstein-Uhlenbeck processes and well-posedness of stochastic Ginzburg-Landau equations

TL;DR

This paper studies the mathematical properties of renormalized powers of Ornstein-Uhlenbeck processes to prove well-posedness and regularity of solutions for stochastic Ginzburg-Landau equations in two and three dimensions.

Contribution

It introduces a rigorous analysis of renormalized powers to establish local existence, uniqueness, and regularity of solutions for stochastic Ginzburg-Landau equations.

Findings

Well-posedness of stochastic Ginzburg-Landau equations in 2D and 3D

Regularity results for solutions

Framework for handling polynomial and quadratic nonlinearities

Abstract

This article analyzes well-definedness and regularity of renormalized powers of Ornstein-Uhlenbeck processes and uses this analysis to establish local existence, uniqueness and regularity of strong solutions of stochastic Ginzburg-Landau equations with polynomial nonlinearities in two space dimensions and with quadratic nonlinearities in three space dimensions.