A variational view on constitutive laws in parabolic problems

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 $\mathcal{A}$-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.

51 pages

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