The sharp minimal time for null controllability of the parabolic spherical Baouendi-Grushin equation on crown ω={α<x3<β} is ln(1/sqrt(1-α²)), with controllability in any positive time if the equator is included.
Analysis of the null controllability of degenerate parabolic systems of Grushin type via the moments method
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Minimal time for null controllability of the parabolic spherical Baouendi-Grushin equation
The sharp minimal time for null controllability of the parabolic spherical Baouendi-Grushin equation on crown ω={α<x3<β} is ln(1/sqrt(1-α²)), with controllability in any positive time if the equator is included.