Burgers equation in the adhesion model

Abstract

We prove the existence and uniqueness of a classical solution to a multidimensional non-potential stochastic Burgers equation with Hölder 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.

COMMUNICATED BY:

• A. Pankov

Keywords:

• Multidimensional non-potential stochastic Burgers equation
• adhesion model

AMS subject classifications:

• 60H15
• 60H10
• 35K59

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of the first-named author was partially supported by RFBR [grant number 18-01-00048].