Geometric Hydrodynamics in Open Problems — Problem 35

Definitions and mathematical statement

The supplied statement refers to a mechanism and an apparatus described in preceding source material that is absent from this record. It also introduces parameters $n_i,m_i,r_i$, but supplies neither their definitions nor their domains, index set, or relationships. The terms "cascade" and "real hydrodynamics" are not mathematically specified in the supplied record.

With these unresolved references retained, the source asks:

1. Does there exist a mechanism describing a cascade in real hydrodynamics that is analogous to the mechanism referred to in the preceding source discussion?
2. Is it possible to define the parameters $n_i,m_i,r_i$ so that the apparatus referred to in that discussion works as intended?

The governing equations, admissible hydrodynamic setting, relevant boundary conditions, meaning of a cascade, comparison mechanism, and required properties of the apparatus are not supplied. Consequently, these questions cannot yet be expressed as a fully specified mathematical existence statement with explicit domains, hypotheses, and quantifiers.

Short English statement

The problem asks whether a previously described mechanism has an analogue for hydrodynamic cascades, and whether parameters $n_i,m_i,r_i$ can be defined to make the associated apparatus work. The missing preceding discussion prevents a precise mathematical formulation.

Sources

• Local UnsolvedMath registry: permanent ID $800836$, source problem code catalogue entry, title Geometric Hydrodynamics in Open Problems --- Problem 35. The supplied record attributes the problem to Khesin, Misiolek, and Modin, with proposed year 2022, and labels it open; this label is supplied registry metadata, not an independently verified mathematical status.
• Khesin, Misiolek, and Modin, Geometric Hydrodynamics in Open Problems (2022), Problem 35. Supplied source URL: https://arxiv.org/abs/2205.01143. The record reports access on 2026-10-16 and extraction by arxiv_latex; these are supplied provenance details, not a claim of independent source consultation.
• Supplied upstream revision: d371ee917ac9647fbb06cd6fc529deec6f3dda82.