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. We prove the existence and uniqueness of global strong solutions to the Cauchy problem of the compressible Stokes approximation equations for any (specific heat ratio) γ > 1 in R when initial data are helically symmetric. Moreover, the large-time behavior of the strong solution and the existence of global weak solutions are obtained simultaneously. The proof is based on a Ladyzhenskaya interpolation type inequality for helically symmetric functions in R and uniform a priori estimtes. The present paper extends Lions’ [17] and Lu, Kazhikhov and Ukai’s [18] existence theorem in R to the three-dimensional helically symmetric case.

Global Helically Symmetric Solutions for the Stokes Approximation Equations for Three-Dimensional Compressible Viscous Flows