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arXiv · 2602.14412

The small Deborah number limit for the compressible fluid-particle flows

Zhendong Fang·Kunlun Qi·Huanyao Wen
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Abstract

In this paper, we consider the hydrodynamic limit for the fluid-particle flows governed by the Vlasov-Fokker-Planck equation coupled with the compressible Navier-Stokes equation as the Deborah number tends to zero. The proof is based on a formal derivation via the Hilbert expansion around the limiting system, the rigorous justification of which is completed by the refined energy estimates involving the macro-micro decomposition. Compared with the existing results obtained by the relative entropy argument ([A. Mellet and A. F. Vasseur, Comm. Math. Phys., 281 (2008), pp. 573-596]), the present work extends to a pointwise convergence of the hydrodynamic limits with an explicit rate for the fluid-particle coupled model.

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Zhendong Fang, Kunlun Qi, Huanyao Wen. 2026-06-25. The small Deborah number limit for the compressible fluid-particle flows. https://arxiv.org/abs/2602.14412

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