On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion
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| Format: | Preprint |
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2025
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| _version_ | 1866912697657851904 |
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| author | Fritz, Marvin Süli, Endre Wohlmuth, Barbara |
| author_facet | Fritz, Marvin Süli, Endre Wohlmuth, Barbara |
| contents | In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation governing the evolution of the probability density function of polymer configurations. The model incorporates nonlocal features to capture subdiffusive and memory-type phenomena. Our main result asserts the existence of global-in-time large-data weak solutions to this nonlocal system. The proof relies on an energy estimate involving a suitable relative entropy, which enables us to handle the critical general non-corotational drag term that couples the two equations. As a side result, we prove nonnegativity of the probability density function. A crucial step in our analysis is to establish strong convergence of the sequence of Galerkin approximations by a combination of techniques, involving a novel compactness result for nonlocal PDEs. Lastly, we prove the uniqueness of weak solutions with sufficient regularity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_06570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion Fritz, Marvin Süli, Endre Wohlmuth, Barbara Analysis of PDEs 35Q30, 35Q84, 35R11, 60G22, 82C31, 82D60 In this work, we study a class of nonlocal-in-time kinetic models of incompressible dilute polymeric fluids. The system couples a macroscopic balance of linear momentum equation with a mezoscopic subdiffusive Fokker-Planck equation governing the evolution of the probability density function of polymer configurations. The model incorporates nonlocal features to capture subdiffusive and memory-type phenomena. Our main result asserts the existence of global-in-time large-data weak solutions to this nonlocal system. The proof relies on an energy estimate involving a suitable relative entropy, which enables us to handle the critical general non-corotational drag term that couples the two equations. As a side result, we prove nonnegativity of the probability density function. A crucial step in our analysis is to establish strong convergence of the sequence of Galerkin approximations by a combination of techniques, involving a novel compactness result for nonlocal PDEs. Lastly, we prove the uniqueness of weak solutions with sufficient regularity. |
| title | On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion |
| topic | Analysis of PDEs 35Q30, 35Q84, 35R11, 60G22, 82C31, 82D60 |
| url | https://arxiv.org/abs/2511.06570 |