Abstract
We study the spherically symmetric motion of viscous barotropic gas surrounding a ball. The basic equation is the compressible Navier-Stokes equation. We are interested in the density distribution which contacts with vacuum at a finite radius. This is a free boundary problem. After rewriting the equation in the Lagrangean coordinate, we construct approximate solutions by discretizing the mass variable. Passing to a limit, we find a global weak solution.
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References
M. Okada, Free boundary value problems for the equation of one-dimensional motion of viscous gas. Japan J. Appl. Math.,6 (1989), 161–177.
H. Fujita-Yashima et R. Benabidallah, Equation à symétrie sphérique d'un gaz visqueux et calorifère avec la surface libre. Preprint 2.88 (616), Dip. Mat. Pisa, Gennaio, 1992.
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Okada, M., Makino, T. Free boundary problem for the equation of spherically symmetric motion of viscous gas. Japan J. Indust. Appl. Math. 10, 219 (1993). https://doi.org/10.1007/BF03167573
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DOI: https://doi.org/10.1007/BF03167573