# The global weak solutions of compressible Euler equation with spherical symmetry

## Authors

- Received:

DOI: 10.1007/BF03167276

- Cite this article as:
- Makino, T., Mizohata, K. & Ukai, S. Japan J. Indust. Appl. Math. (1992) 9: 431. doi:10.1007/BF03167276

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## Abstract

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 case*n*>-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 case*n*>-2. We will do this, however, only for the case of spherical symmetry with γ=1, by using a modified Glimm’s method.