2021 # Vectorial variational problems in L
^{∞} constrained by the Navier–Stokes equations*

**Abstract:** We study a minimisation problem in L
p
and L
∞ for certain cost functionals, where the class of admissible mappings is constrained by the Navier–Stokes equations. Problems of this type are motivated by variational data assimilation for atmospheric flows arising in weather forecasting. Herein we establish the existence of PDE-constrained minimisers for all p, and also that L
p
…

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2022

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