Entropy principle for the moment systems of degree \(\alpha\) associated to the Boltzmann equation. Critical derivatives and non-controllable boundary data
Using simple stationary problems, the authors show that the entropy principle fails in general, if all the non-equilibrium variables are of the same order of magnitude. This is due to the fact that there exist some derivatives on non-equilibrium variables (critical derivatives) that are not small along the solutions. This property can be used to fix the non-controllable boundary data in such a manner that the critical derivatives are kept small for the solution that we may choose.
scientific article; zbMATH DE number 1747932