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arXiv:2007.15758 [math.AP]AbstractReferencesReviewsResources

Eulerian dynamics in multi-dimensions with radial symmetry

Changhui Tan

Published 2020-07-30Version 1

We study the global wellposedness of pressure-less Eulerian dynamics in multi-dimensions, with radially symmetric data. Compared with the 1D system, a major difference in multi-dimensional Eulerian dynamics is the presence of the spectral gap, which is difficult to control in general. We propose a new pair of scalar quantities that provides a significant better control of the spectral gap. Two applications are presented. (i) the Euler-Poisson equations: we show a sharp threshold condition on initial data that distinguish global regularity and finite time blowup; (ii) the Euler-alignment equations: we show a large subcritical region of initial data that leads to global smooth solutions.

Comments: 34 pages, 6 figures
Categories: math.AP
Subjects: 35Q35
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