Communications in Mathematical Sciences

Volume 18 (2020)

Number 5

Decay estimate to a compressible Euler system with non-local velocity alignment

Pages: 1469 – 1475



Lining Tong (Department of Mathematics, Shanghai University, Shanghai, China)

Li Chen (Department of Mathematics, University of Mannheim, Germany)


In this paper, the asymptotic behavior of the solutions for compressible Euler system with a non-local interaction term is studied. Using velocity damping to restrain the singularity caused by the anisotropic interaction between individuals, the exponential decay estimate of the solutions is obtained.


compressible Euler system, exponential decay, velocity alignment

2010 Mathematics Subject Classification

35L65, 35Q70

L. Tong was supported by the National Natural Science Foundation of China (grant nos. 11901379 and 11771274).

Received 22 May 2019

Accepted 14 March 2020

Published 23 September 2020