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The dynamic phi^4_3 model comes down from infinity
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Mourrat, J-C. and Weber, Hendrik (2017) The dynamic phi^4_3 model comes down from infinity. Communications in Mathematical Physics, 356 (3). pp. 673-753. doi:10.1007/s00220-017-2997-4 ISSN 0010-3616.
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Official URL: https://doi.org/10.1007/s00220-017-2997-4
Abstract
We prove an a priori bound for the dynamic $\Phi^4_3$ model on the torus wich is independent of the initial condition. In particular, this bound rules out the possibility of finite time blow-up of the solution. It also gives a uniform control over solutions at large times, and thus allows to construct invariant measures via the Krylov-Bogoliubov method. It thereby provides a new dynamic construction of the Euclidean $\Phi^4_3$ field theory on finite volume. Our method is based on the local-in-time solution theory developed recently by Gubinelli, Imkeller, Perkowski and Catellier, Chouk. The argument relies entirely on deterministic PDE arguments (such as embeddings of Besov spaces and interpolation), which are combined to derive energy inequalities.
| Item Type: | Journal Article | ||||||||
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| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Journal or Publication Title: | Communications in Mathematical Physics | ||||||||
| Publisher: | Springer | ||||||||
| ISSN: | 0010-3616 | ||||||||
| Official Date: | December 2017 | ||||||||
| Dates: |
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| Volume: | 356 | ||||||||
| Number: | 3 | ||||||||
| Page Range: | pp. 673-753 | ||||||||
| DOI: | 10.1007/s00220-017-2997-4 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||
| Date of first compliant deposit: | 27 July 2017 | ||||||||
| Date of first compliant Open Access: | 29 January 2018 |
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