The small Deborah number limit for the compressible fluid-particle flows
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915799818567680 |
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| author | Fang, Zhendong Qi, Kunlun Wen, Huanyao |
| author_facet | Fang, Zhendong Qi, Kunlun Wen, Huanyao |
| contents | 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 limit is valid globally in time provided that the initial perturbation is small in a neighborhood of a steady state. 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 provides a stronger pointwise convergence of the hydrodynamic limits with an explicit rate for the fluid-particle coupled model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14412 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The small Deborah number limit for the compressible fluid-particle flows Fang, Zhendong Qi, Kunlun Wen, Huanyao Analysis of PDEs Primary 35Q99, 35B25, 35Q30, 35B40. Second: 82C40, 76N10 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 limit is valid globally in time provided that the initial perturbation is small in a neighborhood of a steady state. 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 provides a stronger pointwise convergence of the hydrodynamic limits with an explicit rate for the fluid-particle coupled model. |
| title | The small Deborah number limit for the compressible fluid-particle flows |
| topic | Analysis of PDEs Primary 35Q99, 35B25, 35Q30, 35B40. Second: 82C40, 76N10 |
| url | https://arxiv.org/abs/2602.14412 |