Asymptotic flocking dynamics of Relativistic-Cucker-Smale particles immersed in incompressible Navier-Stokes equations
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912276853817344 |
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| author | Yan, Shenglun Zou, Weiyuan |
| author_facet | Yan, Shenglun Zou, Weiyuan |
| contents | In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the time-asymptotic behavior of the proposed model in $\mathbb{T}^3$. It is shown that the coupled system exhibits an exponential alignment under some specific assumptions, and that weak solutions exist globally for general initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12056 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic flocking dynamics of Relativistic-Cucker-Smale particles immersed in incompressible Navier-Stokes equations Yan, Shenglun Zou, Weiyuan Analysis of PDEs In this paper, we propose a coupled system describing the interaction between the Relativistic Cucker-Smale model and the incompressible Navier-Stokes equations via a drag force, and establish a global existence theory as well as the time-asymptotic behavior of the proposed model in $\mathbb{T}^3$. It is shown that the coupled system exhibits an exponential alignment under some specific assumptions, and that weak solutions exist globally for general initial data. |
| title | Asymptotic flocking dynamics of Relativistic-Cucker-Smale particles immersed in incompressible Navier-Stokes equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.12056 |