Work

Well-Posedness of the generalised Dean–Kawasaki Equation with correlated noise on bounded domains

Year: 2024

Type: article

Abstract: In this paper, we extend the notion of stochastic kinetic solutions introduced in arXiv:2108.08858 to establish the well-posedness of stochastic kinetic solutions of generalized Dean-Kawasaki equations with correlated noise on bounded, $C^2$-domains with Dirichlet boundary conditions. The results apply to a wide class of non-negative boundary data, which is based on certain a priori estimates for the solutions, that encompasses all non-negative constant functions including zero and all smooth functions bounded away from zero.

Source: Stochastic Processes and their Applications

DOI: 10.1016/j.spa.2024.104503

Author: Shyam Popat

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,420

Funder: Engineering and Physical Sciences Research Council

Awards: G1600321425, EPSRC Centre for Doctoral Training in Mathematics of Random Systems: Analysis, Modelling and Simulation