Global solutions to the cylindrically symmetric rotating motion of isentropic gases

Abstract

We construct global solutions to the Euler equations of compressible isentropic gas dynamics with cylindrically symmetric rotating structure. A shock capturing numerical scheme is introduced to compute such a flow and to construct approximate solutions. The convergence and consistency of the approximate solutions generated from this scheme to the global solutions are proved with the aid of a compensated compactness framework. Earlier work of the authors, which controlled the geometrical source terms, especially as they pertain to radial flow in an unbounded region,\(\left| {\vec x} \right|\) ≥ 1, is extended here to the 3 × 3 system of cylindrically symmetric rotating flow. Arbitrary data withLα bounds are allowed in these results.