Quantitative approximation of the Vlasov(-Fokker-Planck)-Navier-Stokes system by stochastic particle systems
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913050675642368 |
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| author | Goudenège, Ludovic Olivera, Christian Planas, Gabriela Richard, Alexandre |
| author_facet | Goudenège, Ludovic Olivera, Christian Planas, Gabriela Richard, Alexandre |
| contents | This paper is concerned with a fluid-particle system given by the incompressible Navier-Stokes equations coupled with the Vlasov(-Fokker-Planck) equation through a drag force. Such a model arises naturally in the study of aerosols, sprays, and more generally two-phase flows. In dimensions $d\in \{2,3\}$, we establish a rate of convergence for a system of $N$ interacting stochastic particles coupled with a fluid, towards the Vlasov(-Fokker-Planck)-Navier-Stokes system, as $N\to \infty$. The case of particles with a noise that vanishes as $N\to \infty$ is considered and leads specifically to the Vlasov-Navier-Stokes system. More precisely, we prove that the empirical measure associated with the particle system converges to the Vlasov(-Fokker-Planck) component, while the fluid velocity converges to the Navier-Stokes component of the coupled system. The proofs combine stochastic calculus and PDE techniques to establish energy estimates and commutator estimates for both the discrete and continuous systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18871 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative approximation of the Vlasov(-Fokker-Planck)-Navier-Stokes system by stochastic particle systems Goudenège, Ludovic Olivera, Christian Planas, Gabriela Richard, Alexandre Probability Analysis of PDEs This paper is concerned with a fluid-particle system given by the incompressible Navier-Stokes equations coupled with the Vlasov(-Fokker-Planck) equation through a drag force. Such a model arises naturally in the study of aerosols, sprays, and more generally two-phase flows. In dimensions $d\in \{2,3\}$, we establish a rate of convergence for a system of $N$ interacting stochastic particles coupled with a fluid, towards the Vlasov(-Fokker-Planck)-Navier-Stokes system, as $N\to \infty$. The case of particles with a noise that vanishes as $N\to \infty$ is considered and leads specifically to the Vlasov-Navier-Stokes system. More precisely, we prove that the empirical measure associated with the particle system converges to the Vlasov(-Fokker-Planck) component, while the fluid velocity converges to the Navier-Stokes component of the coupled system. The proofs combine stochastic calculus and PDE techniques to establish energy estimates and commutator estimates for both the discrete and continuous systems. |
| title | Quantitative approximation of the Vlasov(-Fokker-Planck)-Navier-Stokes system by stochastic particle systems |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2604.18871 |