A variational view on constitutive laws in parabolic problems

2025/06/30 by Schiffer, Stefan, Xylander, Espen
#35Q30 #49J45 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.23910

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 \mathscrA-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.

Citations

• Non-classical solutions of the p-Laplace equation
• Non-uniqueness of Leray solutions of the forced Navier-Stokes equations
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?

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