Boundary gradient estimates for subsonic solutions of compressible transonic potential flows

Eun Heui Kim

doi:10.3934/proc.2007.2007.573

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2007, Volume 2007: 573-579. Doi: 10.3934/proc.2007.2007.573 open access

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Boundary gradient estimates for subsonic solutions of compressible transonic potential flows

Eun Heui Kim^1,

1.
Department of Mathematics and Statistics, California State University, Long Beach, Long Beach, CA 90840-1001

Received: September 2006

Revised: August 2007

Published: August 2007

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Abstract

We establish boundary gradient estimates for a solution for selfsimilar transonic potential flow on the subsonic region. The gradient estimates enable us to verify the ellipticity of the solution in the region. We consider both convex and general domains. We provide the sufficient conditions to show that the flow becomes transonic.

Keywords:

Boundary gradient estimates; transonic potential flow; degenerate; ellipticity; self-similar.

Mathematics Subject Classification: Primary: 35J70; 35L65 ; Secondary: 35Q35.

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