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Theoretical analysis reveals four candidate viscosity operators on ellipsoids using thin shell limits, demonstrating that resulting operators depend directly on the chosen averaging method.
In this paper, we derive four new candidates for an intrinsic viscosity operator on an ellipsoid by using the heuristic of the thin shell limit along the scaling direction of the ellipsoid. We show that the general method of the thin shell limit through the asymptotic expansion depends on the averaging method used. We consider both the homogeneous Navier and Hodge boundary conditions. We also obtain a geometric representation of these two boundary conditions.
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Chan et al. (2026) studied this question.
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