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arXiv · 2506.23910

A variational view on constitutive laws in parabolic problems

Stefan Schiffer·Espen Xylander
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Abstract

We consider a variational approach to solve parabolic problems by minimising a functional over time and space. To achieve existence results we investigate the notion of $\mathscr{A}$-quasiconvexity for non-homogeneous operators in anisotropic spaces. The abstract theory is then applied to formulate a variational solution concept for the non-Newtonian Navier--Stokes equations.

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Stefan Schiffer, Espen Xylander. 2025-06-30. A variational view on constitutive laws in parabolic problems. https://doi.org/10.1515/acv-2025-0076

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