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 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.
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Makino, T., Mizohata, K. & Ukai, S. The global weak solutions of compressible Euler equation with spherical symmetry. Japan J. Indust. Appl. Math. 9, 431–449 (1992). https://doi.org/10.1007/BF03167276
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DOI: https://doi.org/10.1007/BF03167276