Burgers equation in the adhesion model

TL;DR

This paper proves the existence and uniqueness of solutions to a multidimensional stochastic Burgers equation, advancing the mathematical understanding of the adhesion model in cosmology without assuming potential velocity flow.

Contribution

It establishes the well-posedness of a non-potential stochastic Burgers equation, removing the potentiality assumption previously questioned in physics.

Findings

Proved existence and uniqueness of classical solutions

Extended the model to non-potential flows in multiple dimensions

Reinforced the mathematical foundation of the adhesion model

Abstract

We prove the existence and uniqueness of a classical solution to a multidimensional non-potential stochastic Burgers equation with H\"older continuous initial data. Our motivation is the adhesion model in the theory of formation of the large-scale structure of the universe. Importantly, we drop the assumption on the potentiality of the velocity flow that has been questioned in physics literature.