Vectorial variational problems in L ^∞ constrained by the Navier–Stokes equations*

Abstract We study a minimisation problem in L p and ∞ for certain cost functionals, where the class of admissible mappings is constrained by Navier–Stokes equations. Problems this type are motivated variational data assimilation atmospheric flows arising weather forecasting. Herein we establish existence PDE-constrained minimisers all , also that converge to as → ∞. further show solve an Euler–Lagrange system. Finally, special constructed via approximation shown divergence PDE system involving measure coefficients, which divergence-form counterpart corresponding non-divergence Aronsson–Euler