A functional integral approach to shock wave solutions of the Euler equations with spherical symmetry. II (Q1924453)

This is a continuation of the author's work [Commun. Math. Phys. 171, No. 3, 607-638 (1995; Zbl 0840.35062)] where we introduced a new norm and a functional integral approach to prove a uniform bound for a model problem of Euler equation in \(R^3\) with spherical symmetry. In order to overcome the geometric effects of spherical symmetry which leads to a non-integrable source term, we considered an infinite reflection problem and solved it by considering the cancellations between reflections of different orders. In this paper, we consider a system which describes the isentropic spherically symmetric motion of gas surrounding a solid star with radius 1 and mass \(M\). The wave curves for this problem are no longer continuous and there is an extra term in the wave interaction estimates. By introducing a new norm, we prove a similar result as in the above work.