## Differential and Integral Equations

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

Jong Uhn Kim

#### 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