Nonlinear well-posedness of the 11-moment polyatomic-gas system

Prove a complete nonlinear well-posedness theorem for the GENERIC-compatible 11-moment system for polyatomic gases, taking into account the hyperbolic inviscid subsystem, rank-deficient parabolic dissipation, and non-negative entropy production identified in the model.

Background

The proposed GENERIC-compatible 11-moment model has a hyperbolic inviscid part for realizable states and dissipative constitutive terms that produce a rank-deficient diffusion operator. The authors therefore classify the full system as hyperbolic--incompletely parabolic and note that analytical treatment may require structural conditions such as symmetrizability, dissipativity, and the Shizuta--Kawashima condition.

Although the paper establishes the model's formal mathematical and thermodynamic structure, it does not establish local or global nonlinear well-posedness. A rigorous theory would need to determine whether the identified hyperbolic and partially dissipative structures suffice to control the undamped modes of the full nonlinear system.

References

In the present work we do not attempt to prove a complete nonlinear well-posedness theorem for the 11-moment system. Instead, we identify the structural ingredients needed for such an analysis: hyperbolicity of the inviscid part for realizable states, rank-deficient parabolic dissipation, and non-negative entropy production. A rigorous well-posedness theory for the full nonlinear system is left for future work.

— Non-equilibrium modelling of polyatomic gases: generic framework and 11-moment model  (2608.24100 - Ahmad et al., 25 Aug 2026) in Section "Mathematical structure" in Section 3, immediately before Section "Comparative Analysis of Models"