Ancient solution

In mathematics, an ancient solution to a differential equation is a solution that can be extrapolated backwards to all past times, without singularities. That is, it is a solution "that is defined on a time interval of the form (−∞, T)."^[1]

The term was introduced by Richard Hamilton in his work on the Ricci flow.^[2] It has since been applied to other geometric flows^[3][4][5][6] as well as to other systems such as the Navier–Stokes equations^[7][8] and heat equation.^[9]