Abstract
AbstractWe establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations in the absence of vacuum in $$(1 + H^s) \times H^{s-1}$$
(
1
+
H
s
)
×
H
s
-
1
with $$s \ge 1$$
s
≥
1
. We achieve this by a reduction via the Madelung transform to the previous global-in-time well-posedness result for the Gross–Pitaevskii equation in Koch and Liao (Adv Math 377, 2021; Adv Math 420, 2023). Our core result is a local bilipschitz equivalence of the relevant function spaces, which enables the transfer of results between the two equations.
Funder
Deutsche Forschungsgemeinschaft
Karlsruher Institut für Technologie (KIT)
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Physics and Astronomy,General Mathematics
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