A maximum principle for compressible flow on a surface

Lesley M. Sibner, Robert J. Sibner
1978 Proceedings of the American Mathematical Society  
We show that the speed of a steady, irrotational, subsonic now on a surface cannot attain its maximum at a point of positive Gauss curvature. In his work on curvature and homology, Bochner [3] obtained a formula for the Laplacian of the norm of a harmonic form on an orientable Riemannian manifold in terms of the curvature of the manifold. In this paper we obtain a corresponding formula for p-harmonic forms which describe compressible flows and will use this result to show that a steady,
more » ... t a steady, irrotational subsonic fluid flow on a surface cannot attain its maximum speed at a point of positive Gaussian curvature. 2. Subsonic flows. Letting as the speed of the flow. From physical considerations we make the rather general assumptions (cf. [1]) that the density p of the fluid is a function of Q alone which is bounded above and
doi:10.1090/s0002-9939-1978-0482795-2 fatcat:lazlyrbfxfhubacck7cywbhjtu