Hydrodynamic limit of a kinetic flocking model with nonlinear velocity alignment
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916514810036224 |
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| author | Black, McKenzie Tan, Changhui |
| author_facet | Black, McKenzie Tan, Changhui |
| contents | We investigate a class of Vlasov-type kinetic flocking models featuring nonlinear velocity alignment. Our primary objective is to rigorously derive the hydrodynamic limit leading to the compressible Euler system with nonlinear alignment. This study builds upon the work by Figalli and Kang [Anal. PDE, 12(3), 843-866, 2018], which addressed the scenario of linear velocity alignment using the relative entropy method. The introduction of nonlinearity gives rise to an additional discrepancy in the alignment term during the limiting process. To effectively handle this discrepancy, we employ the monokinetic ansatz in conjunction with the relative entropy approach. Furthermore, our analysis reveals distinct nonlinear alignment behaviors between the kinetic and hydrodynamic systems, particularly evident in the isothermal regime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16641 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit of a kinetic flocking model with nonlinear velocity alignment Black, McKenzie Tan, Changhui Analysis of PDEs 35Q35, 35Q70, 35B25 We investigate a class of Vlasov-type kinetic flocking models featuring nonlinear velocity alignment. Our primary objective is to rigorously derive the hydrodynamic limit leading to the compressible Euler system with nonlinear alignment. This study builds upon the work by Figalli and Kang [Anal. PDE, 12(3), 843-866, 2018], which addressed the scenario of linear velocity alignment using the relative entropy method. The introduction of nonlinearity gives rise to an additional discrepancy in the alignment term during the limiting process. To effectively handle this discrepancy, we employ the monokinetic ansatz in conjunction with the relative entropy approach. Furthermore, our analysis reveals distinct nonlinear alignment behaviors between the kinetic and hydrodynamic systems, particularly evident in the isothermal regime. |
| title | Hydrodynamic limit of a kinetic flocking model with nonlinear velocity alignment |
| topic | Analysis of PDEs 35Q35, 35Q70, 35B25 |
| url | https://arxiv.org/abs/2312.16641 |