Differential and Integral Equations

On the regularity of the velocity potential in two-dimensional transonic flow

Jong Uhn Kim

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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.

Article information

Source
Differential Integral Equations, Volume 11, Number 1 (1998), 107-132.

Dates
First available in Project Euclid: 1 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367414138

Mathematical Reviews number (MathSciNet)
MR1608000

Zentralblatt MATH identifier
1007.35065

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics
Secondary: 35B65: Smoothness and regularity of solutions 35M10: Equations of mixed type 76H05: Transonic flows

Citation

Kim, Jong Uhn. On the regularity of the velocity potential in two-dimensional transonic flow. Differential Integral Equations 11 (1998), no. 1, 107--132. https://projecteuclid.org/euclid.die/1367414138


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