On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion

Marvin Fritz; Endre Süli; Barbara Wohlmuth

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arXiv · 2511.06570

On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion

Marvin Fritz·Endre Süli·Barbara Wohlmuth

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Abstract

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.

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Marvin Fritz, Endre Süli, Barbara Wohlmuth. 2025-11-09. On the well-posedness of a nonlocal kinetic model for dilute polymers with anomalous diffusion. https://arxiv.org/abs/2511.06570

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