Journal article
On a novel gradient flow structure for the aggregation equation
- Abstract:
- The aggregation equation arises naturally in kinetic theory in the study of granular media, and its interpretation as a 2-Wasserstein gradient flow for the nonlocal interaction energy is well-known. Starting from the spatially homogeneous inelastic Boltzmann equation, a formal Taylor expansion reveals a link between this equation and the aggregation equation with an appropriately chosen interaction potential. Inspired by this formal link and the fact that the associated aggregation equation also dissipates the kinetic energy, we present a novel way of interpreting the aggregation equation as a gradient flow, in the sense of curves of maximal slope, of the kinetic energy, rather than the usual interaction energy, with respect to an appropriately constructed transportation metric on the space of probability measures.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 541.7KB, Terms of use)
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- Publisher copy:
- 10.1007/s00526-024-02692-x
Authors
- Publisher:
- Springer
- Journal:
- Calculus of Variations and Partial Differential Equations More from this journal
- Volume:
- 63
- Issue:
- 5
- Article number:
- 126
- Publication date:
- 2024-05-05
- Acceptance date:
- 2024-03-06
- DOI:
- EISSN:
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1432-0835
- ISSN:
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0944-2669
- Language:
-
English
- Keywords:
- Pubs id:
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1920296
- Local pid:
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pubs:1920296
- Deposit date:
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2024-03-28
Terms of use
- Copyright holder:
- Esposito et al.
- Copyright date:
- 2024
- Rights statement:
- Copyright © 2024, The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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