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Comparison principles for self-similar potential flow. (English) Zbl 1235.35056

Summary: We establish a strong comparison principle, as well as a weak comparison principle and a Hopf-type lemma, for elliptic solutions of the self-similar potential flow equation. A major difference from the steady case is that the coefficients of the equation depend on the potential function itself, as well as its gradient. We employ the divergence structure and other features of the equation to derive the results.

MSC:

35B51 Comparison principles in context of PDEs
76N15 Gas dynamics (general theory)
76G25 General aerodynamics and subsonic flows
35Q35 PDEs in connection with fluid mechanics
35J62 Quasilinear elliptic equations
35L65 Hyperbolic conservation laws
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