Global classical existence for the high-dimensional hydrodynamic Cucker–Smale model

Prove global existence of a classical solution for the general high-dimensional hydrodynamic Cucker–Smale model referenced in the paper.

Background

The paper states that its framework can also be applied to the hydrodynamic Cucker–Smale model studied in the cited literature. However, it distinguishes this applicability from a full global classical well-posedness result for the general high-dimensional hydrodynamic model.

The unresolved issue concerns global existence of classical solutions in the general high-dimensional setting, rather than the measure-valued or weak-solution theory developed for the kinetic model in the paper.

References

In particular, our results can also be applied to the hydrodynamic CS model in , although the global existence of a classical solution in the general high-dimensional hydrodynamic CS model is still open (see ).

— Weak flocking for phase-spatially extended kinetic Cucker-Smale equation in a confining force field  (2608.22709 - Ha et al., 24 Aug 2026) in Section 6, Conclusion

A global theory for arbitrary smooth non-vacuum initial data remains largely open.

— Global regularity for the unidirectional Euler-alignment system with supercritical dissipation  (2609.25748 - Tan et al., 22 Sep 2026) in Section 1, Introduction, paragraph following the discussion of the spectral-gap obstruction