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February  2010, 27(1): 357-368. doi: 10.3934/dcds.2010.27.357

Unique subsonic compressible potential flows in three -dimensional ducts

Li Liu 1,

1. 

Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China

Received  June 2009 Revised  December 2009 Published  February 2010

We establish the uniqueness of subsonic potential flows in a three-dimensional finite duct, a semi-infinite duct and an infinite duct with quadrate sections, as well as flows in half space and whole space. Moreover, some extremum principles for the related elliptic equations are proved under suitable assumptions in unbounded domains.
Keywords: subsonic flow., Harnack inequality, unbounded domain, extremum principle, uniqueness, potential flow equation.
Mathematics Subject Classification: Primary: 35J25; Secondary: 76N1.
Citation: Li Liu. Unique subsonic compressible potential flows in three -dimensional ducts. Discrete & Continuous Dynamical Systems, 2010, 27 (1) : 357-368. doi: 10.3934/dcds.2010.27.357
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