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
Jong Uhn Kim. "On the regularity of the velocity potential in two-dimensional transonic flow." Differential Integral Equations 11 (1) 107 - 132, 1998. https://doi.org/10.57262/die/1367414138
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