On the analytical aspects of inertial particle motion

Oliver D. Street, Dan Crisan

incompletemedium confidence

Category: Not specified
Journal tier: Strong Field
Processed: Sep 28, 2025, 12:56 AM
arXiv Links: Abstract ↗PDF ↗

Audit review

The paper’s global well-posedness argument for the integral Maxey–Riley system succeeds in spirit but contains a gap: in its uniqueness and local-contraction steps it effectively ignores the term [Mu(y1)−Mu(y2)]w, which requires a spatial Lipschitz bound for Mu that is not included in Assumption (*). The candidate solution gives a clean Banach fixed-point proof and correct a priori bounds, but it implicitly strengthens Assumption (*) by assuming Mu is Lipschitz in y (it asserts this follows from (*), which it does not). Thus, the paper needs an added regularity hypothesis (or a different argument), while the model needs to state its stronger assumption explicitly.

Referee report (LaTeX)

\textbf{Recommendation:} major revisions

\textbf{Journal Tier:} strong field

\textbf{Justification:}

The paper’s strategy—local fixed-point for a re-centered map P, fractional Grönwall bounds, and continuation—is apt for handling the Basset kernel and makes a valuable contribution to the global theory. However, the present proofs implicitly require a spatial Lipschitz bound for Mu (or an alternative uniqueness device) that is not part of Assumption (*). This gap appears in the contraction/uniqueness estimates and should be addressed either by strengthening the hypotheses or by replacing Banach’s contraction with an argument that tolerates merely continuous Mu. With these corrections, the results should be sound.