Leaderless Collective Cell Motion and Macroscopic Limits

Definitions and mathematical statement

The supplied research question is: Can collective cell movement develop without a leader, and what macroscopic limits result from microscopic or mesoscopic models of such movement?

Its two requested targets are:

1. Establish whether collective cell movement can emerge in a model without a leader.
2. Identify and justify macroscopic limits of microscopic or mesoscopic models exhibiting such movement.

A precise mathematical proposition cannot be extracted uniquely from this record. No model equations, admissible class of models, spatial domain, initial conditions, boundary conditions, interaction rules, or stochastic assumptions are supplied. Neither "collective movement" nor "leader" is given a mathematical criterion. In particular, the record does not specify whether leaderlessness concerns the absence of a distinguished agent, externally prescribed direction, or some other mechanism.

For the limiting question, the limiting parameter, scaling, macroscopic variables, candidate limiting equations, time interval, and mode of convergence are unspecified. The source also does not determine whether the desired conclusion concerns the existence of one suitable model or a statement quantified over a specified class of models. These missing choices remain unresolved; the questions above are a statement of the supplied research program, not a fully quantified theorem or conjecture.

Short English statement

The problem asks whether cells can develop coordinated movement without a leader and how microscopic or mesoscopic descriptions lead to macroscopic equations. The supplied record leaves the models, coordination and leadership criteria, and limiting procedure unspecified, so a unique precise mathematical statement requires further source clarification.

Sources

• Local registry: supplied UnsolvedMath source record, permanent ID $30002573$, source problem code catalogue entry, title Leaderless Collective Cell Motion and Macroscopic Limits, in the Oberwolfach Reports Open Problems collection. No individual proposer is supplied; the proposed year is recorded as 2014.
• Supplied report citation: Mini-Workshop: Mathematical Models for Cancer Cell Migration (2015), Oberwolfach Reports, DOI 10.4171/owr/2014/19, pp. 1075--1109. https://doi.org/10.4171/owr/2014/19. The background attributes the question to workshop open-problem discussions. No problem-specific page or passage is supplied.
• Supplied literature reference, labeled "Leaderless collective motion": https://doi.org/10.1016/S0167-2789(03)00102-7.
• Supplied literature reference, labeled "Hydrodynamic limit": https://doi.org/10.1137/15M1035665.
• Supplied literature reference, labeled "Macroscopic collective-motion models": https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.32/.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the problem partially solved and reports rigorous and computational realizations of leaderless collective motion in self-organized particle models, hydrodynamic limits for important alignment systems, and the absence of a universal macroscopic limit covering all collective-cell mechanisms. This is supplied dated curation derived from the supplied OWR material, not an independently verified assessment. Its time-sensitive status and cited claims require independent verification.
• The registry labels the statement "exact" and describes it as retained byte-for-byte, clear, self-contained, and publication-ready. These are supplied verification claims, not independent source verification or confirmation that the mathematical formulation is complete.