Mean-field limits: from particle descriptions to macroscopic equations
We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulate...
| Hlavní autoři: | , |
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| Médium: | Journal article |
| Jazyk: | English |
| Vydáno: |
Springer Nature
2021
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| _version_ | 1826275556708057088 |
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| author | Carrillo de la Plata, JA Choi, Y-P |
| author_facet | Carrillo de la Plata, JA Choi, Y-P |
| author_sort | Carrillo de la Plata, JA |
| collection | OXFORD |
| description | We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions. |
| first_indexed | 2024-03-06T23:00:32Z |
| format | Journal article |
| id | oxford-uuid:61f09077-ce6b-488f-9565-e1ee954b39ef |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:00:32Z |
| publishDate | 2021 |
| publisher | Springer Nature |
| record_format | dspace |
| spelling | oxford-uuid:61f09077-ce6b-488f-9565-e1ee954b39ef2022-03-26T18:03:11ZMean-field limits: from particle descriptions to macroscopic equations Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:61f09077-ce6b-488f-9565-e1ee954b39efEnglishSymplectic ElementsSpringer Nature2021Carrillo de la Plata, JAChoi, Y-PWe rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. Crucially, we make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions. |
| spellingShingle | Carrillo de la Plata, JA Choi, Y-P Mean-field limits: from particle descriptions to macroscopic equations |
| title | Mean-field limits: from particle descriptions to macroscopic equations
|
| title_full | Mean-field limits: from particle descriptions to macroscopic equations
|
| title_fullStr | Mean-field limits: from particle descriptions to macroscopic equations
|
| title_full_unstemmed | Mean-field limits: from particle descriptions to macroscopic equations
|
| title_short | Mean-field limits: from particle descriptions to macroscopic equations
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| title_sort | mean field limits from particle descriptions to macroscopic equations |
| work_keys_str_mv | AT carrillodelaplataja meanfieldlimitsfromparticledescriptionstomacroscopicequations AT choiyp meanfieldlimitsfromparticledescriptionstomacroscopicequations |