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arXiv · 2508.07415

Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force

Roman Shvydkoy·Trevor Teolis
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Abstract

We study a coupled Fokker-Planck--Navier-Stokes (FPNS) system modeling the dynamics of interacting particles suspended in a viscous incompressible fluid, where the coupling occurs through a locally averaged Brinkman drag force. Our main result is the unconditional alignment and synchronization of particle and fluid velocities for all weak solutions, in any dimension, on the periodic domain. The proof leverages a new entropy method and a hypocoercivity framework, which together yield quantitative decay estimates and prevent density concentration, a key obstacle in previous analyses. Our approach applies to a broad class of nonlocal alignment protocols, including the Cucker-Smale model. We also prove develop well-posedness theory for global weak solutions with hypoelliptic regularization in any dimension, and global strong solutions in two dimensions.

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Roman Shvydkoy, Trevor Teolis. 2025-08-10. Unconditional alignment of solutions to the Fokker-Planck-Navier-Stokes system with locally averaged Brinkman force. https://arxiv.org/abs/2508.07415

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