Global $L^{\infty}$ solutions of the compressible Euler equations with spherical symmetry
Tsuge, Naoki
J. Math. Kyoto Univ., Tome 46 (2006) no. 4, p. 457-524 / Harvested from Project Euclid
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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.
Publié le : 2006-05-15
Classification:  35Q35,  35B45,  35D05,  76N10 
@article{1250281746,
     author = {Tsuge, Naoki},
     title = {Global $L^{\infty}$ solutions of the compressible Euler equations with spherical symmetry},
     journal = {J. Math. Kyoto Univ.},
     volume = {46},
     number = {4},
     year = {2006},
     pages = { 457-524},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250281746}
}

Tsuge, Naoki. Global $L^{\infty}$ solutions of the compressible Euler equations with spherical symmetry. J. Math. Kyoto Univ., Tome 46 (2006) no. 4, pp.  457-524. http://gdmltest.u-ga.fr/item/1250281746/