We study the spherically symmetric motion of viscous barotropic gas surrounding a solid ball. We are interested in the density distribution which contacts with the vacuum at a ¡ radius. This is a free boundary problem. We obtained the existence of a global weak solution with some regular properties. We can show that such a solution is unique.We are investigating the equations { 0 0 0u ) [Ou +uOU~ , Op =. ['02u 20u p = ap'~, where u, a, "7 are positive constants and 1 < ~, _~ 2. These equations govern the spherically symmetric motion of viscous barotropic gas. We consider these equations in r _~ 1 with the boundary condition ul~=l =0 and the initial conditions P I~=0 = p0(r), u I~=0 = u~ Since we are interested in the class of initial data which includes the stationary solutions = , u=0~
(R < r)* This work was completed during her stay at Universit 91 degli studi di Ferrara which was supported by GNFM of Italian CNR.
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