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Invariant measures as probabilistic tools in the analysis of nonlinear ODEs and PDEs
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Ammari, Zied, Farhat, Shahnaz and Sohinger, Vedran (2023) Invariant measures as probabilistic tools in the analysis of nonlinear ODEs and PDEs. In: INdAM Quantum Meetings (IQM22), Milan, Italy, Mar-May 2022. Published in: Proceedings of IQM22 , 57 pp. 301-317. ISBN 9789819958931. doi:10.1007/978-981-99-5894-8_12 ISSN 2281-518X.
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WRAP-invariant-measures-probabilistic-tools-analysis-nonlinear-ODEs-PDEs-2023.pdf - Accepted Version Embargoed item. Restricted access to Repository staff only until 1 December 2024. Contact author directly, specifying your specific needs. - Requires a PDF viewer. Download (417Kb) |
Official URL: https://doi.org/10.1007/978-981-99-5894-8_12
Abstract
We consider finite and infinite dimensional Hamiltonian systems and note that Gibbs measures are the unique probability measures satisfying an entropy and a classical Kubo–Martin–Schwinger (KMS) condition. Furthermore, we discuss Bourgain’s method consisting of using Gibbs measures as conservation laws at low regularity in order to construct global solutions for some nonlinear dispersive PDEs almost surely. It is then argued that such an approach is very general and works for abstract initial value problems and invariant measures. Note that the definition of invariance here does not require an a priori flow and is inspired by the KMS principle.
Item Type: | Conference Item (Paper) | ||||||
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Alternative Title: | |||||||
Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Probabilities, Measure theory, Hamiltonian operator, Differential equations, Partial, Differential equations, Nonlinear | ||||||
Series Name: | Springer INdAM Series | ||||||
Journal or Publication Title: | Proceedings of IQM22 | ||||||
Publisher: | Springer | ||||||
ISBN: | 9789819958931 | ||||||
ISSN: | 2281-518X | ||||||
Book Title: | Quantum Mathematics I | ||||||
Official Date: | 1 December 2023 | ||||||
Dates: |
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Volume: | 57 | ||||||
Page Range: | pp. 301-317 | ||||||
DOI: | 10.1007/978-981-99-5894-8_12 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Re-use Statement: | “This version of the article has been accepted for publication, after peer review (when applicable) but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at:https://doi.org/10.1007/978-981-99-5894-8_12 Use of this Accepted Version is subject to the publisher’s Accepted Manuscript terms of use https://www.springernature.com/gp/open-research/policies/acceptedmanuscript-terms”." | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 29 September 2023 | ||||||
Conference Paper Type: | Paper | ||||||
Title of Event: | INdAM Quantum Meetings (IQM22) | ||||||
Type of Event: | Other | ||||||
Location of Event: | Milan, Italy | ||||||
Date(s) of Event: | Mar-May 2022 | ||||||
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