The global weak solutions of compressible Euler equation with spherical symmetry
We shall study the compressible Euler equation which describes the motion of an isentropic gas. Many global existence theorems have been obtained for the one dimensional case. On the other hand, little is known for the casen>-2. No global weak solutions have been known to exist, but only local classical solutions. In this paper, we will present global weak solutions first for the casen>-2. We will do this, however, only for the case of spherical symmetry with γ=1, by using a modified Glimm’s method.
Key wordscompressible Euler equation shock wave Riemann invariant Glimm’s difference scheme
- X. Ding, G. Chen and P. Luo, Convergence of the Lax-Friedrichs scheme for isentropic gas dynamics, (III). Acta Math. Sci.,6, (1986), 75–120.Google Scholar
- P.D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves. SIAM Reg. Conf. Lecture 11, Philadelphia, 1973.Google Scholar