Global $L^{\infty}$ solutions of the compressible Euler equations with spherical symmetry

• Autores: Naoki Tsuge
• Localización: Journal of mathematics of Kyoto University, ISSN 0023-608X, Vol. 46, Nº 3, 2006, págs. 457-524
• Idioma: inglés
• DOI: 10.1215/kjm/1250281746
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• Resumen

  • We study the compressible Euler equations with spherical symmetry surrounding a solid ball. For the spherically symmetric flow, the global existence of $L^{\infty}$ entropy weak solutions has not yet obtained except a special case. In this paper, we prove the existence of global solutions in the more general case. We construct approximate solutions by using a modified Godunov scheme. The main point is to obtain an $L^{\infty}$ bound for the approximate solutions.