Nonlinear stability of spherical self-similar flows to the compressible Euler equations

We present the nonlinear stability of spherical self-similar flows arising from the uniform expansion of a spherical piston toward still gas. If the perturbation of the expansion speed of the piston is sufficiently small compared with the strength of the leading shock, a global weak solution of the isentropic compressible Euler system exists in the region between the spherical piston and the leading shock under the structural condition on the shock Mach number and the nondimensional piston speed. Moreover, we show that the perturbed flow tends to the corresponding self-similar flow time-asymptotically. Our analysis is based on the modified Glimm scheme.