Global hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system with large data
Abstract
In this paper, we aim to investigate the global-in-time hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system for light particles. With a modified micro-macro decomposition yielding uniform a priori estimates with respect to the Deborah number ε, we prove that the solution of the original system tends to that of the target system, i.e., the incompressible Navier-Stokes/Kramers-Smoluchowski system, as Deborah number goes to zero, and that quantitative convergence rates are obtained in the Lx,v,t∞ norm. Compared with the existing results that the convergence is from ``weak solution" to ``strong solution", the convergence results in the present work are further developed globally in time from ``strong solution" to ``strong solution" with vacuum (i.e., the macroscopic particle density may vanish at far field or at any point) and large initial data for both the original system and the target system. In addition, the ill-prepared initial data for the microscopic component of the kinetic quantity are allowed.
Related
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- Global existence and vanishing viscosity limit of the compressible Navier-Stokes-Vlasov-Fokker-Planck system in critical spaces
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- Incompressible limit for non-isentropic compressible Euler-Navier-Stokes two-phase flow model in R^3
BibTeX
@misc{li2026global,
title = {{Global hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system with large data}},
author = {Jian Li and Huanyao Wen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25696},
eprint = {2610.25696},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25696},
}
RIS
TY - UNPB
TI - Global hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system with large data
AU - Jian Li
AU - Huanyao Wen
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25696
UR - https://arxiv.org/abs/2610.25696
AB - In this paper, we aim to investigate the global-in-time hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system for light particles. With a modified micro-macro decomposition yielding uniform a priori estimates with respect to the Deborah number ε, we prove that the solution of the original system tends to that of the target system, i.e., the incompressible Navier-Stokes/Kramers-Smoluchowski system, as Deborah number goes to zero, and that quantitative convergence rates are obtained in the L_x,v,t^∞ norm. Compared with the existing results that the convergence is from ``weak solution" to ``strong solution", the convergence results in the present work are further developed globally in time from ``strong solution" to ``strong solution" with vacuum (i.e., the macroscopic particle density may vanish at far field or at any point) and large initial data for both the original system and the target system. In addition, the ill-prepared initial data for the microscopic component of the kinetic quantity are allowed.
ER -