Displaying items by tag: optimal decay rates
Monday, 12 February 2024 10:27
Global well-posedness and asymptotic behavior for the Euler-alignment system with pressure
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 | |
Download the Published Version | |
This work is supported by NSF grants DMS #2108264 and DMS #2238219 |
Published in
Research
Tagged under