Ancient solution explained

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 ."^[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]

Notes and References

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2. Hamilton, Richard S. The formation of singularities in the Ricci flow. Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), 7–136, Int. Press, Cambridge, MA, 1995
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