---
tag: 0QXM0A9878
kind: concept
name: Picard–Lindelöf hypotheses
msc: [34A12]
sources:
  - url: https://en.wikipedia.org/wiki/Picard%E2%80%93Lindel%C3%B6f_theorem
    locator: Theorem
---

## Summary

The Picard–Lindelöf hypotheses on a vector field are continuity in time, a Lipschitz condition in space and a bound near the initial point. They also ask for a short enough time interval.
They are the conditions of the [[Picard–Lindelöf theorem|0P6KRD5B7A]]. See the [[definition|0J7HF2PF1H]].