Coupled Vlasov and non-Newtonian fluid dynamics: existence and large-time behavior
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912546734211072 |
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| author | Choi, Young-Pil Jung, Jinwook Wróblewska-Kamińska, Aneta |
| author_facet | Choi, Young-Pil Jung, Jinwook Wróblewska-Kamińska, Aneta |
| contents | We study a coupled kinetic-non-Newtonian fluid system on the periodic domain ${\mathbb T}^3$, where particles evolve by a Vlasov equation and interact with an incompressible power-law fluid through a drag force. We prove the global existence of weak solutions for all $p > \frac{8}{5}$, where $p > 1$ denotes the power-law exponent of the fluid's stress-strain relation. Under an additional uniform boundedness assumption on the particle density, we also establish large-time decay of a modulated energy functional measuring deviation from velocity alignment. The decay rate is algebraic when $p > 2$ and exponential when $\frac{6}{5} \le p \le 2$, reflecting the role of fluid dissipation in the large-time dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_15460 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coupled Vlasov and non-Newtonian fluid dynamics: existence and large-time behavior Choi, Young-Pil Jung, Jinwook Wróblewska-Kamińska, Aneta Analysis of PDEs 35Q70, 76A05 We study a coupled kinetic-non-Newtonian fluid system on the periodic domain ${\mathbb T}^3$, where particles evolve by a Vlasov equation and interact with an incompressible power-law fluid through a drag force. We prove the global existence of weak solutions for all $p > \frac{8}{5}$, where $p > 1$ denotes the power-law exponent of the fluid's stress-strain relation. Under an additional uniform boundedness assumption on the particle density, we also establish large-time decay of a modulated energy functional measuring deviation from velocity alignment. The decay rate is algebraic when $p > 2$ and exponential when $\frac{6}{5} \le p \le 2$, reflecting the role of fluid dissipation in the large-time dynamics. |
| title | Coupled Vlasov and non-Newtonian fluid dynamics: existence and large-time behavior |
| topic | Analysis of PDEs 35Q70, 76A05 |
| url | https://arxiv.org/abs/2508.15460 |