On a novel gradient flow structure for the aggregation equation
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 revea...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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Springer
2024
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| _version_ | 1811139486951669760 |
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| author | Esposito, A Gvalani, RS Schlichting, A Schmidtchen, M |
| author_facet | Esposito, A Gvalani, RS Schlichting, A Schmidtchen, M |
| author_sort | Esposito, A |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-04-09T03:57:42Z |
| format | Journal article |
| id | oxford-uuid:4f0189a9-b972-454c-a47b-c79e4b6ba86e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:06:52Z |
| publishDate | 2024 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:4f0189a9-b972-454c-a47b-c79e4b6ba86e2024-06-04T10:27:59ZOn a novel gradient flow structure for the aggregation equationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4f0189a9-b972-454c-a47b-c79e4b6ba86eEnglishSymplectic ElementsSpringer2024Esposito, AGvalani, RSSchlichting, ASchmidtchen, MThe 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. |
| spellingShingle | Esposito, A Gvalani, RS Schlichting, A Schmidtchen, M On a novel gradient flow structure for the aggregation equation |
| title | On a novel gradient flow structure for the aggregation equation |
| title_full | On a novel gradient flow structure for the aggregation equation |
| title_fullStr | On a novel gradient flow structure for the aggregation equation |
| title_full_unstemmed | On a novel gradient flow structure for the aggregation equation |
| title_short | On a novel gradient flow structure for the aggregation equation |
| title_sort | on a novel gradient flow structure for the aggregation equation |
| work_keys_str_mv | AT espositoa onanovelgradientflowstructurefortheaggregationequation AT gvalanirs onanovelgradientflowstructurefortheaggregationequation AT schlichtinga onanovelgradientflowstructurefortheaggregationequation AT schmidtchenm onanovelgradientflowstructurefortheaggregationequation |