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arXiv · 2208.11786

Swarming: hydrodynamic alignment with pressure

Eitan Tadmor
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Abstract

We study the swarming behavior of hydrodynamic alignment. Alignment reflects steering towards a weighted average heading. We consider the class of so-called $p$-alignment hydrodynamics, based on $2p$-Laplacians, and weighted by a general family of symmetric communication kernels. The main new aspect here is the long time emergence behavior for a general class of pressure tensors without a closure assumption, beyond the mere requirement that they form an energy dissipative process. We refer to such pressure laws as `entropic', and prove the flocking of $p$-alignment hydrodynamics, driven by singular kernels with general class of entropic pressure tensors. These results indicate the rigidity of alignment in driving long-time flocking behavior despite the lack of thermodynamic closure.

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Eitan Tadmor. 2022-08-24. Swarming: hydrodynamic alignment with pressure. https://arxiv.org/abs/2208.11786

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