Global weak solutions of the compressible Euler equation with spherical symmetry (II)
We study the spherically symmetric motion of isothermal gas surrounding a ball. Recently we constructed global weak solutions for the initial boundary value problem in , but the class of the initial data considered there was not wide enough to include the stationary solutions for which the density is constant on the whole space. In this paper we will extend our preceding result to a wider class of the initial data so that it includes such stationary solutions. To do this, we will present a modification of Glimm’s method in which the mesh lengths for approximate solutions are not uniform.
Key wordscompressible Euler equation shock wave Riemann invariant Glimm’s difference scheme
Unable to display preview. Download preview PDF.