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Entropy status of computed statistical solutions for Euler and conservation laws

Determine whether statistically computed solutions of the incompressible Euler equations and multidimensional systems of conservation laws produced by current numerical methods satisfy entropy conditions or are entropy-maximizing solutions in the Boltzmann–Gibbs/Kullback–Leibler sense.

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Background

The authors note that statistical solutions of the incompressible Euler equations and multidimensional conservation laws can be computed numerically. However, due to ill-posedness and lack of convergence, it is unclear whether these numerically obtained statistical solutions meet entropy criteria or maximize entropy.

Clarifying the entropy properties of these computed statistical solutions would connect computational practice with the maximum entropy framework advocated in the paper.

References

However, due to the lack of the well-posedness of these problems and the lack of convergence of their numerical approximations, it is not known whether these solutions are entropy or entropy maximizing solutions.

— A Principle of Maximum Entropy for the Navier-Stokes Equations (2402.14240 - Chen et al., 22 Feb 2024) in Section 1.1