Comparison principles for self-similar potential flow

Chen, Gui-Qiang; Feldman, Mikhail

doi:10.1090/S0002-9939-2011-10937-7

Comparison principles for self-similar potential flow
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by Gui-Qiang G. Chen and Mikhail Feldman

Proc. Amer. Math. Soc. 140 (2012), 651-663

DOI: https://doi.org/10.1090/S0002-9939-2011-10937-7

Published electronically: June 21, 2011

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Abstract:

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.

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