Global hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system with large data

Jian Li; Huanyao Wen

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arXiv · 2610.25696

Global hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system with large data

Jian Li·Huanyao Wen

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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 $\varepsilon$, 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 $L_{x,v,t}^\infty$ 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.

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BibTeX RIS

Jian Li, Huanyao Wen. 2026-10-19. Global hydrodynamic limit of the incompressible Navier-Stokes/Vlasov-Fokker-Planck system with large data. https://arxiv.org/abs/2610.25696

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