2022/08/24 by Tadmor, Eitan · 1 citation
#35Q35 #76N10 #92D25 #Adaptation and Self-Organizing Systems (nlin.AO) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences
paper · doi:10.48550/arxiv.2208.11786
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.