On blowup phenomena of solutions to the Euler equations for Chaplygin gases

In this paper, we are concerned with the blowup phenomena of solutions to the isentropic Euler equations for Chaplygin gases. By the method of phase portrait and Liapunov functions, we first obtain the blowup results of the spherically symmetric solutions to the equations in the multi-dimensional case. For one-dimensional Chaplygin gases, some solutions globally in time and blowup phenomena are derived simultaneously by the constructing method.