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 <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi mathvariant="script">𝒜</m:mi> </m:math> {\mathscr{A}} -quasiconvexity for non-homogeneous operators in anisotropic spaces. The abstract theory is then applied to formulate a variational solution concept for the generalised Navier–Stokes equations.