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The small Deborah number limit for the compressible fluid...
[Submitted on 16 Feb 2026 (v1), last revised 25 Jun 2026 (this v · 2026-06-26 · via math updates on arXiv.org

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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.

Submission history

From: Kunlun Qi [view email]
[v1] Mon, 16 Feb 2026 02:40:41 UTC (33 KB)
[v2] Thu, 25 Jun 2026 04:18:03 UTC (30 KB)