Resolution of the spherical piston problem for compressible isentropic gas dynamics via a self-similar viscous limit

Source abstract

This paper proves the existence of solutions to the spherical piston problem for isentropic gas dynamics with equation of state p ( p ) = Ap γ , γ≧ 1. The method of analysis is to replace the usual viscosity ε with ε t , thus permitting a search for self-similar viscous limits. The main result of the paper is that self-similar viscous limits are proved to exist and converge to a solution to the piston problem when N = 1, 2, 3 space dimensions.