Communications in Mathematical Sciences

Volume 21 (2023)

Number 3

Global-in-time classical solutions to two-dimensional axisymmetric Euler system with swirl

Pages: 829 – 857



Geng Lai (Department of Mathematics, Shanghai University, Shanghai, China )

Mi Zhu (Department of Mathematics, Shanghai University, Shanghai, China)


We study global-in-time classical solutions to the two-dimensional (2D) compressible Euler system with axial symmetry. We derive several groups of suitable characteristic decompositions for the 2D axisymmetric compressible Euler system. Using these characteristic decompositions, we find several classes of expanding initial data to ensure the existence of global-in-time classical solutions. These solutions have an expanding vacuum region centered at the origin.


axisymmetric Euler system, classical solution, characteristic decomposition, vacuum

2010 Mathematics Subject Classification

35L60, 35L65, 35L67

This work is partially supported by National Natural Science Foundation of China (NSFC 12071278).

Received 22 August 2021

Accepted 15 August 2022

Published 27 February 2023