Wave maps equation explained

In mathematical physics, the wave maps equation is a geometric wave equation that solves

D ^{\alpha} \partial _{\alpha} u = 0

where

D is a connection.^{[1] [2]}

It can be considered a natural extension of the wave equation for Riemannian manifolds.^[3]

Notes and References

1. Tataru. Daniel. Rough solutions for the wave maps equation. American Journal of Mathematics. 1 January 2005. 127. 2. 293–377. 10.1353/ajm.2005.0014. 10.1.1.631.6746. 53521030.
2. 1065.35199 . Tataru . Daniel . The wave maps equation . . New Series . 41 . 2 . 185–204 . 2004 . 10.1090/S0273-0979-04-01005-5 . free .
3. Web site: Tao . Terence . Wave Maps (preprint) . 2023-10-04 . Department of Mathematics, UCLA.