Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryThe Navier–Stokes equations, formulated in the 19th century, describe how fluids like air and water move and are the basis of weather prediction, aircraft design, and blood-flow modeling. Despite how thoroughly they're used in practice, nobody has proven that their solutions in three dimensions stay smooth (well-behaved) for all time rather than developing a singularity — or found a case where one does.
The question, scope, and sources behind this Registry record.
In three spatial dimensions, given smooth, physically reasonable initial velocity data, do smooth solutions to the Navier–Stokes equations exist for all time — or can a singularity (blow-up) occur in finite time?
Change a parameter to stress-test whether a proposed result is still inside the published specification. This is an audit aid, not a proof checker.
This record has no editable parameters. Read the formal question and assumptions before challenging it.
Current frontiers derived from accepted Claims.
The frontier is not sacred
Most progress starts with a disagreement that survives contact with evidence. If you can push the known lower bound up or pull the upper bound down, show us the work.
≥ when you have shown that at least this value is achievable.≤ when you have shown that anything above this value is impossible.No vibes. State the value, define the scope, and link the paper, proof, code, or reproduction that lets another person check it. Editors review every challenge before the public record changes.
Challenge this recordAssertions tied to evidence, attribution, and review.
No accepted Claims are recorded for this Limit yet.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.