Work

Dean–Kawasaki equation with initial condition in the space of positive distributions

Year: 2024

Type: article

Abstract: We show that the Dean–Kawasaki equation does not admit non-trivial solutions in the space of tempered measures. More specifically, we consider martingale solutions taking values, and with initial conditions, in the subspace of measures admitting infinite mass and satisfying some integrability conditions. Following work by the first author, Lehmann and von Renesse (Electron Commun Probab 24:3916340, 2019), we show that the equation only admits solutions if the initial measure is a discrete measure. Our result extends the previously mentioned works by allowing measures with infinite mass.

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-024-01018-w

Authors: Vitalii Konarovskyi, Fenna Müller

Institutions: Universität Hamburg, Institute of Mathematics, Max Planck Institute for Mathematics in the Sciences, Leipzig University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Deutsche Forschungsgemeinschaft, Universität Bielefeld, Max-Planck-Institut für Mathematik in den Naturwissenschaften