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• W3162131180 abstract "We study a minimisation problem in $L^p$ and $L^infty$ 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 $L^p$ minimisers converge to $L^infty$ minimisers as $ptoinfty$. We further show that $L^p$ minimisers solve an Euler-Lagrange system. Finally, all special $L^infty$ minimisers constructed via approximation by $L^p$ minimisers are shown to solve a divergence PDE system involving measure coefficients, which is a divergence-form counterpart of the corresponding non-divergence Aronsson-Euler system." @default.
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• W3162131180 date "2021-05-13" @default.
• W3162131180 modified "2023-09-27" @default.
• W3162131180 title "Vectorial variational problems in $L^infty$ constrained by the Navier-Stokes equations" @default.
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