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GLOBAL SOLUTIONS TO THE COMPRESSIBLE EULER EQUATIONS WITH GRAVITATIONAL SOURCE

NAOKI TSUGE

Department of Information Systems and Management, Hiroshima Institute of Technology, 2-1-1 Miyake, Saeki-ku, Hiroshima, Hiroshima 731-5193, Japan

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https://doi.org/10.1142/S0219891608001507Cited by:2 (Source: Crossref)

Abstract

We study the compressible Euler equations in spherical symmetry with a gravitational source surrounding a solid ball. Despite its physical importance, this problem has not received much attention until now. We prove the global existence of weak solutions by constructing approximate solutions and using a modified Godunov scheme. The main point is to obtain a sup-norm bound for the approximate solutions.

Keywords:

AMSC: Primary 35L65, Primary 76N10, Secondary 35B45, Secondary 35L60, Secondary 76N15

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