Displaying items by tag: optimal decay rates

Xiang Bai, Changhui Tan and Liutang Xue

Journal of Differential Equations, Volume 407, pp. 269-310 (2024).

Abstract

We study the Cauchy problem of the compressible Euler system with strongly singular velocity alignment. We establish a global well-posedness theory for the system with small smooth initial data. Additionally, we derive asymptotic emergent behaviors for the system, providing time decay estimates with optimal decay rates. Notably, the optimal decay rate we obtain does not align with the corresponding fractional heat equation within our considered range, where the parameter \(\alpha\in(0,1)\). This highlights the distinct feature of the alignment operator.

	doi:10.1016/j.jde.2024.06.020
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	This work is supported by NSF grants DMS #2108264 and DMS #2238219