Blowup Of The Spherically Symmetric Solutions To The 2-D Full Compressible Euler Equations

In this paper, we are concerned with the blowup problem of the spherically sym-metric solutions to the 2-D full compressible Euler system. When the initial data are of small perturbations with respect to a constant state, we obtain the precise bound of the lifespan. For the 2-D isentropic Euler system with the symmetric rotation, S.Alinhac in [5] has established the lifespan of the small data symmetric solutions. Our focus is on the non-isentropic case in this paper. The main ingredients are: at first we construct a suitable approximate solution, then by utilizing the norms which are introduced in [6-7] for studying the 3-D blowup problems and combining some delicate analysis, we can obtain the precise lower bound of the lifespan. Finally we may show that the lower bound is also the upper bound of the lifespan by exploiting some techniques in ordinary differential equations.