Global well-posedness of strong solution to the kinetic Cucker-Smale model with external potential field

Linglong Du; Anqi Du; Zhengyan Luo; Linglong Du; Anqi Du; Zhengyan Luo

doi:10.3934/nhm.2025021

Networks and Heterogeneous Media

2025, Volume 20, Issue 2: 460-481. doi: 10.3934/nhm.2025021

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Global well-posedness of strong solution to the kinetic Cucker-Smale model with external potential field

1.
School of Mathematics and Statistics and Institute for Nonlinear Science, Donghua University, Shanghai, China
2.
School of Mathematics and Statistics, Donghua University, Shanghai, China

Received: 24 March 2025 Revised: 29 April 2025 Accepted: 07 May 2025 Published: 14 May 2025
35Q84, 35D35, 35B30, 35Q92

In this paper, we studied the initial problem of the kinetic Cucker-Smale model with noise, driven by pairwise alignment interactions under the influence of external potential field. Without the general compact support or smallness assumption on the initial datum, we established the global existence of strong solution. The proof was based on weighted energy estimates.
- kinetic Cucker-Smale model with noise,
- external potential field,
- global well-posedness
Citation: Linglong Du, Anqi Du, Zhengyan Luo. Global well-posedness of strong solution to the kinetic Cucker-Smale model with external potential field[J]. Networks and Heterogeneous Media, 2025, 20(2): 460-481. doi: 10.3934/nhm.2025021

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Abstract

In this paper, we studied the initial problem of the kinetic Cucker-Smale model with noise, driven by pairwise alignment interactions under the influence of external potential field. Without the general compact support or smallness assumption on the initial datum, we established the global existence of strong solution. The proof was based on weighted energy estimates.

References

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