2021
DOI: 10.48550/arxiv.2107.00709
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Global solutions to multi-dimensional topological Euler alignment systems

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 global smooth solutions -para… Show more

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