Replace analyticity of the forcing by rotation invariance of its curl

Determine whether the real-analyticity assumption on the spatial variables of the forcing in Theorem 1.1 can be replaced by rotation invariance of the curl of the forcing, while retaining the theorem’s regularity conclusion for asymptotically axisymmetric Navier–Stokes solutions.

Background

Theorem 1.1 uses spatial analyticity of the forcing to extend exact axisymmetry from a shrinking core to the entire spatial domain through the identity theorem. The authors observe that the hypotheses nevertheless imply rotation invariance of the curl of the forcing. They explicitly leave unresolved whether this weaker symmetry condition is sufficient to replace analyticity in the theorem.