Global Solutions to Multi-dimensional Topological Euler Alignment Systems

  title={Global Solutions to Multi-dimensional Topological Euler Alignment Systems},
  author={Daniel Lear and David N. Reynolds and Roman Shvydkoy},
  journal={Annals of PDE},
Abstract. We present a systematic approach to regularity theory of the multi-dimensional Euler alignment systems with topological diffusion introduced in [27]. While these systems exhibit flocking behavior emerging from purely local communication, bearing direct relevance to empirical field studies, global and even local well-posedness has proved to be a major challenge in multi-dimensional settings due to the presence of topological effects. In this paper we reveal two important classes of… 


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  • R. Shvydkoy
  • Mathematics
    Journal of Dynamics and Differential Equations
  • 2018
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