Solvability of the divergence-curl problem with no-slip boundary is equivalent to orthogonality of vorticity to pseudo-harmonic fields, with an explicit countable family given for the 3D exterior sphere problem.
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On the Multi-Dimensional Divergence-Curl Problem and Its Connection with Pseudo-Harmonic Fields
Solvability of the divergence-curl problem with no-slip boundary is equivalent to orthogonality of vorticity to pseudo-harmonic fields, with an explicit countable family given for the 3D exterior sphere problem.