Dean-Kawasaki equation with initial condition in the space of positive distributions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914997275197440 |
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| author | Konarovskyi, Vitalii Müller, Fenna |
| author_facet | Konarovskyi, Vitalii Müller, Fenna |
| contents | 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 [arXiv:1806.05018], 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_10006 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dean-Kawasaki equation with initial condition in the space of positive distributions Konarovskyi, Vitalii Müller, Fenna Probability 60G57, 60H15, 60K35 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 [arXiv:1806.05018], 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. |
| title | Dean-Kawasaki equation with initial condition in the space of positive distributions |
| topic | Probability 60G57, 60H15, 60K35 |
| url | https://arxiv.org/abs/2311.10006 |