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We establish global-in-time well-posedness of the one-dimensionalhydrodynamic Gross-Pitaevskii equations in the absence of vacuum in $(1 + H^s)\times H^{s-1}$ with $s \geq 1$. We achieve this by a reduction via theMadelung transform to the previous global-in-time well-posedness result for theGross-Pitaevskii equation in arXiv:1801.08386v2 [math.AP] andarXiv:2204.06293v1 [math.AP]. Our core result is a local bilipschitzequivalence between the relevant function spaces.

Global-in-time Well-posedness of the One-dimensional Hydrodynamic Gross-Pitaevskii Equations without Vacuum