Math @ Duke

Publications [#337290] of Siming He
Papers Published
 He, S; Tadmor, E, Global regularity of twodimensional flocking hydrodynamics,
Comptes Rendus Mathematique, vol. 355 no. 7
(July, 2017),
pp. 795805, Elsevier BV [doi]
(last updated on 2020/07/12)
Abstract: © 2017 Académie des sciences We study the systems of Euler equations that arise from agentbased dynamics driven by velocity alignment. It is known that smooth solutions to such systems must flock, namely the largetime behavior of the velocity field approaches a limiting “flocking” velocity. To address the question of global regularity, we derive sharp critical thresholds in the phase space of initial configuration that characterizes the global regularity and hence the flocking behavior of such twodimensional systems. Specifically, we prove for that a large class of subcritical initial conditions such that the initial divergence is “not too negative” and the initial spectral gap is “not too large”, global regularity persists for all time.


dept@math.duke.edu
ph: 919.660.2800
fax: 919.660.2821
 
Mathematics Department
Duke University, Box 90320
Durham, NC 277080320

