Displaying items by tag: Radial symmetry

Changhui Tan

SIAM Journal on Mathematical Analysis, Volume 53, No 3, pp. 3040–3071 (2021).

Abstract

We study the global wellposedness of pressureless Eulerian dynamics in multidimensions, with radially symmetric data. Compared with the one-dimensional system, a major difference in multidimensional 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 significantly 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.

	doi:10.1137/20M1358682
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	This work is supported by NSF grant DMS #1853001