Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Conical shock waves for an isentropic Euler system

Shuxing Chena1 and Dening Lia2

a1 Institute of Mathematics, Fudan University, Shanghai, People's Republic of China (

a2 Department of Mathematics, 4098 Armstrong Hall, West Virginia University, Morgantown, WV 26506, USA (


Conical shock waves are generated as sharp conical solid projectiles fly supersonically in the air. We study such conical shock waves in steady supersonic flow using an isentropic Euler system. The stability of such attached conical shock waves for non-symmetrical conical projectiles and non-uniform incoming supersonic flow is established. Meanwhile, the existence of the solution to the Euler system with such attached conical shock as a free boundary is also proved for solid projectiles close to a regular solid cone.

(Received March 12 2004)

(Accepted March 23 2005)