MiS Preprint Repository
We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
The Dean--Kawasaki equation with initial condition in the space of positive distributions
Vitalii Konarovskyi and Fenna MüllerAbstract
We show that the Dean--Kawasaki equation does not admit nontrivial 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 (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.
- Received:
- 16.11.23
- Published:
- 16.11.23
- MSC Codes:
- 60G57, 60H15, 60K35
- Keywords:
- Dean-Kawasaki Equation, SPDE, Tempered Measures