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1998 On the regularity of the velocity potential in two-dimensional transonic flow
Jong Uhn Kim
Differential Integral Equations 11(1): 107-132 (1998).

Abstract

We present a new result on the regularity of the velocity potential in transonic gas dynamics of two space dimensions. We prove that the velocity potential is $C^{\infty}$ in a neighborhood of a sonic point if the sonic line is locally $C^{\infty}, $ and if the velocity potential is known to be locally $C^4. $ Our main tool is Hörmander's energy method for the Tricomi operator, the commutator estimate of Kato and Ponce, and a result of Berezin for a degenerate hyperbolic equation.

Citation

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Jong Uhn Kim. "On the regularity of the velocity potential in two-dimensional transonic flow." Differential Integral Equations 11 (1) 107 - 132, 1998.

Information

Published: 1998
First available in Project Euclid: 1 May 2013

zbMATH: 1007.35065
MathSciNet: MR1608000

Subjects:
Primary: 35Q35
Secondary: 35B65, 35M10, 76H05

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 1 • 1998
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