Abstract
In this paper, we prove the global existence of small Gevrey-2 solutions to the 3D axially symmetric Prandtl equations. The index 2 is the optimal index for well-posedness result in smooth Gevrey function spaces for data without monotonic assumptions. The novelty of our paper lies in two aspects: one is the tangentially weighted energy construction to match the [Formula: see text] weight in the incompressibility and the other is introducing of the new linearly good unknowns to obtain the fast decay of the lower order Gevrey-2 norms of the solutions and auxiliary functions.
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