Existence of a frequency formula for the axially symmetric cavity problem

Determine whether a frequency formula corresponding to the frequency formula in reference [aw] exists for the three-dimensional axially symmetric Neumann-type Bernoulli cavity problem.

Background

The paper contrasts the cavity problem with obstacle problems, where frequency estimates can be obtained for the difference between a solution and its blow-down limit. For the Neumann-type Bernoulli cavity problem, the authors report that analogous arguments have not succeeded and that the available evidence suggests that the corresponding frequency formula may not exist. The existence or nonexistence of such a formula therefore remains unresolved.

References

For example, while it is possible (see ) to obtain frequency estimates for the difference of the solution and its blow-down limit in the obstacle problem, we have tried in vain to do something similar in the cavity problem; on the contrary we have found evidence pointing towards a frequency formula corresponding to the one in to be non-existent in the cavity problem.

— Complete Rigidity at infinity and Existence of the Levinson Cavity  (2608.18913 - Li et al., 19 Aug 2026) in Section 1, subsection “Cavity flows”