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June2005 Global Helically Symmetric Solutions for the Stokes Approximation Equations for Three-Dimensional Compressible Viscous Flows
Zhenhua Gao, Song Jiang, Jing Li
Methods Appl. Anal. 12(2): 135-152 (June2005).

Abstract

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) $\gamma > 1$ in $\Bbb R^3$ 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 $\Bbb R^3$ and uniform a priori estimtes. The present paper extends Lions’ and Lu, Kazhikhov and Ukai’s existence theorem in $\Bbb R^2$ to the three-dimensional helically symmetric case.

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Zhenhua Gao. Song Jiang. Jing Li. "Global Helically Symmetric Solutions for the Stokes Approximation Equations for Three-Dimensional Compressible Viscous Flows." Methods Appl. Anal. 12 (2) 135 - 152, June2005.

Information

Published: June2005
First available in Project Euclid: 5 April 2007

zbMATH: 1110.35067
MathSciNet: MR2257524

Subjects:
Primary: 35Q30, 35Q35

Rights: Copyright © 2005 International Press of Boston

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Vol.12 • No. 2 • June2005
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