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Demonstrates a variational method to solve parabolic problems, indicating new solutions for fluid dynamics equations.
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> {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.
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Schiffer et al. (2026) studied this question.
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