On Classical Solutions of the Compressible Euler Equations for Generalized Chaplygin Gas with Qualitative Analysis

In this paper, exact classical solutions of the original three-dimensional compressible Euler equations for generalized Chaplygin gas are constructed by means of the ansatz of the fluid velocity u(t, x) = A' (t) A(-1()t) x. The qualitative analysis of a matrix ordinary differential equation reveals that the obtained exact solutions induce both unique smooth global-in-time and finite-time blowup exact solutions for given initial data. Moreover, the blowup mechanisms in the induced examples are discussed.