Cauchy data

Cauchy data refers to the initial conditions needed to determine a solution to a differential equation, typically specifying the state of a system at a starting point. For example, in physics, it might include an object's initial position and velocity. In mathematics, it involves defining functions and their derivatives at a particular moment or surface, serving as the starting information to predict future behavior of the system governed by the differential equation. Essentially, Cauchy data provides the necessary "initial snapshot" to uniquely determine the evolution of the system over time.