Piston Problems of Two-Dimensional Chaplygin Gas

In this paper, the authors study the piston problem for the unsteadytwo-dimensional Euler system for a Chaplygin gas. The angle of thepiston is allowed to vary in a wide range. The piston can be pushedforward into the static gas, or pulled back from the gas. Theglobal existence of solution to the piston problem with any initialspeed is established, and the structures of the global solutions areclearly described. The authors find that for the proceeding pistonproblem the front shock can be detached, attached or even adhere tothe surface of the piston depending on the parameters of the flowand the piston; while for the receding problem the front rarefactionwave is always detached and the concentration will never occur.