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 𝒜 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.
Schiffer et al. (Fri,) studied this question.