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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.03533 |
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| _version_ | 1866911039093735424 |
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| author | Gao, Jincheng Wu, Jiahong Yao, Zheng-an Yu, Ruijia |
| author_facet | Gao, Jincheng Wu, Jiahong Yao, Zheng-an Yu, Ruijia |
| contents | In this work, we study the global-in-time incompressible limit of the compressible FENE dumbbell model on the three-dimensional torus T^3, where the incompressible limit is driven by large volume viscosity. To establish this limit, we develop time-weighted a priori estimates that yield decay rates for strong solutions. A key challenge arises from the fact that increasing the volume viscosity suppresses the decay of high-frequency components, thereby weakening the dissipation of the density and complicating the derivation of uniform-in-time decay estimates. To overcome this difficulty, we introduce a novel momentum-based estimate and show that the incompressible component of the momentum decays faster in time than the velocity itself. Exploiting this enhanced decay, we successfully close the a priori estimates and establish a time-decreasing convergence rate toward the incompressible limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03533 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Incompressible limit for the 3D compressible FENE dumbbell model Gao, Jincheng Wu, Jiahong Yao, Zheng-an Yu, Ruijia Analysis of PDEs Primary: 35Q35, Secondary: 35B40, 76A10, 35Q30 In this work, we study the global-in-time incompressible limit of the compressible FENE dumbbell model on the three-dimensional torus T^3, where the incompressible limit is driven by large volume viscosity. To establish this limit, we develop time-weighted a priori estimates that yield decay rates for strong solutions. A key challenge arises from the fact that increasing the volume viscosity suppresses the decay of high-frequency components, thereby weakening the dissipation of the density and complicating the derivation of uniform-in-time decay estimates. To overcome this difficulty, we introduce a novel momentum-based estimate and show that the incompressible component of the momentum decays faster in time than the velocity itself. Exploiting this enhanced decay, we successfully close the a priori estimates and establish a time-decreasing convergence rate toward the incompressible limit. |
| title | Incompressible limit for the 3D compressible FENE dumbbell model |
| topic | Analysis of PDEs Primary: 35Q35, Secondary: 35B40, 76A10, 35Q30 |
| url | https://arxiv.org/abs/2507.03533 |