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A smooth transonic flow in the plane

Paul D. Smith

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Abstract

The implicit function theorem is used to study a symmetric exterior problem for the gas dynamics equation—an equation of mixed type. The existence of families of smooth C1 solutions is demonstrated. These solutions are families of smooth transonic flows in the plane and are of applied interest. Some of these results have appeared in the literature with an incorrect derivation using the Hodograph mapping. This mapping is not invertible in the transonic case. The methods of this paper do not use the Hodograph mapping and extend to general (e.g., plasma) flows.

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What this paper is about

The implicit function theorem is used to study a symmetric exterior problem for the gas dynamics equation—an equation of mixed type. The existence of families of smooth C1 solutions is demonstrated. These solutions are families of smooth transonic flows in the plane and are of applied interest. Some of these results have appeared in the literature with an incorrect derivation using the Hodograph mapping. This mapping is not invertible in the transonic case. The methods of this paper do not use the Hodograph mapping and extend to general (e.g., plasma) flows.

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Available abstract

The implicit function theorem is used to study a symmetric exterior problem for the gas dynamics equation—an equation of mixed type. The existence of families of smooth C1 solutions is demonstrated. These solutions are families of smooth transonic flows in the plane and are of applied interest. Some of these results have appeared in the literature with an incorrect derivation using the Hodograph mapping. This mapping is not invertible in the transonic case. The methods of this paper do not use the Hodograph mapping and extend to general (e.g., plasma) flows.

Key concepts: Transonic, Hodograph, Mathematics, Plane (geometry), Flow (mathematics), Gas dynamics, Mathematical analysis, Function (biology)

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