Timeline for Which differential equations allow for a variational formulation?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2016 at 21:36 | answer | added | jdelgado | timeline score: 2 | |
| Jan 28, 2015 at 20:26 | comment | added | Ali Taghavi | @ThomasRot May be you would be interested in the following link: arxiv.org/abs/1411.6814v1 | |
| Jul 7, 2013 at 3:38 | comment | added | Thomas Richard | @TerryTao: I thought the no breather theorem was first proved by Perelman, is it already in Hamilton's works ? | |
| Jul 8, 2012 at 7:52 | vote | accept | Thomas Rot | ||
| Jul 6, 2012 at 10:16 | answer | added | Igor Khavkine | timeline score: 23 | |
| Jul 5, 2012 at 20:43 | answer | added | alvarezpaiva | timeline score: 10 | |
| Jul 5, 2012 at 19:53 | comment | added | Terry Tao | Regarding Ricci flow: in retrospect, the existence of gradient shrinking Ricci solitons, and the absence of periodic-up-to-diffeomorphisms "breather" type solutions, was an indication that Ricci flow had a gradient-flow-up-to-diffeomorphism interpretation. One could also build upon this observation to try to guess the functional that gives this gradient flow, by writing down the integrals that vanish for gradient shrinking solitons, and then trying to express those integrals as a gradient-up-to-diffeomorphisms of something, though this is still far from an easy task... | |
| Jul 5, 2012 at 19:49 | comment | added | Terry Tao | Differential equations with a Hamiltonian formulation, automatically have a Lagrangian formulation (formally, at least). Of course, this simply moves the difficulty over to the question of when one can determine that an equation has a Hamiltonian formulation, but in practice, having a conserved integral of motion tends to be a useful clue in this regard... | |
| Jul 5, 2012 at 16:05 | comment | added | Robert Haslhofer | expanding a bit on the comment of Otis: It was of course know that the Ricci flow is not the gradient flow in a strict sense of a diffeo-invariant functional (reason: gradients of diffeo-invariant functionals are always divergence free, the Ricci tensor is not divergence free), so the amazing and surprising discovery of Perelman was that the Ricci flow actually is a gradient flow up to diffeomorphisms. | |
| Jul 5, 2012 at 15:35 | answer | added | Jonny Evans | timeline score: 7 | |
| Jul 5, 2012 at 15:02 | comment | added | Otis Chodosh | Ricci flow was not known to be a gradient flow until Perelman introduced his F-functional. I guess the setting was more complicated here, because there is a big gauge group of diffeomorphisms, but thats an example of where people were not sure if it could be given a variational formulation until it was done so. | |
| Jul 5, 2012 at 13:33 | comment | added | Denis Serre | I'm sure that the answer is yes and that I have read it once. But where ? | |
| Jul 5, 2012 at 11:58 | history | asked | Thomas Rot | CC BY-SA 3.0 |