Timeline for Long wavelength instability: Linear Vs nonlinear phenomenon
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Oct 22, 2017 at 9:21 | answer | added | John Hunter | timeline score: 1 | |
| S Aug 24, 2017 at 22:55 | history | bounty ended | CommunityBot | ||
| S Aug 24, 2017 at 22:55 | history | notice removed | CommunityBot | ||
| Aug 18, 2017 at 13:13 | comment | added | mystupid_acct | Oh. I was hoping it wouldn't take fields medal level work to do what I want to do. | |
| Aug 18, 2017 at 10:40 | comment | added | Andrew | Something like that was done for the Vlasov equation (multidimensional) by Mouhot and Villani, see "On Landau damping", Acta Mathematica, 2011, V. 207, Issue 1, pp 29–201 link.springer.com/article/10.1007/s11511-011-0068-9, or the same article in arXiv. | |
| Aug 16, 2017 at 21:12 | history | edited | mystupid_acct | CC BY-SA 3.0 |
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| S Aug 16, 2017 at 21:10 | history | bounty started | mystupid_acct | ||
| S Aug 16, 2017 at 21:10 | history | notice added | mystupid_acct | Draw attention | |
| Aug 16, 2017 at 18:06 | comment | added | Willie Wong | For the general theory, since you do have linearly stable frequencies, probably what you want to look at are the literature on the construction of invariant manifolds for infinite dimensional dynamical systems. S.N. Chow and Peter Bates are two names that come up a lot in that field, among others. | |
| Aug 16, 2017 at 17:57 | comment | added | Willie Wong | The best you can expect then is that there exists something like a center-stable-manifold. In this paper we studied a situation where there is one unstable mode. The higher frequencies are all in the continuous spectrum, and while we don't have exponential decay (linear stability), we have dispersion (which gives a weak form of stability). And we can prove codimension-1 stability in this setting. | |
| Aug 15, 2017 at 14:48 | comment | added | mystupid_acct | @WillieWong The modes with frequency <c are exponentially unstable. I am basically looking for references where a PDE case has been explored under similar circumstances. | |
| Aug 15, 2017 at 14:26 | comment | added | Willie Wong | The answer would obviously depend on what $N$ is. You can easily cook up (finite) systems of ODEs with either behavior. In particular, what do you know about the linear stability of $f_0$ for frequency $< c$? | |
| Aug 14, 2017 at 20:57 | history | edited | mystupid_acct | CC BY-SA 3.0 |
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| Aug 14, 2017 at 20:48 | history | asked | mystupid_acct | CC BY-SA 3.0 |