Timeline for Short-time Existence/Uniqueness for Non-linear Schrodinger with Loss of Several Derivatives
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Aug 21, 2010 at 8:01 | history | edited | Piero D'Ancona | CC BY-SA 2.5 |
added 1204 characters in body
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| Aug 20, 2010 at 22:34 | vote | accept | Chris Woodward | ||
| Aug 20, 2010 at 21:48 | comment | added | Chris Woodward | (ctd) So it seems my problem is closest to (3) in Piero's answer, and in fact it seems what I need to do is try to find for which Gevrey class of initial conditions is good. Do you have a recommended reference involving Gevrey initial conditions with loss of derivatives in non-linear Schrodinger? I would be very happy to show uniqueness for $G^s$ initial condition for some $s > 1$. | |
| Aug 20, 2010 at 21:48 | comment | added | Chris Woodward | Thanks Piero and Deane! (1) In my particular equation the potential is obtained from an expression involving the fourth derivatives of the square of the wave-function, by solving a second-order Poisson equation. So if $\psi$ is in $H^s$, then $V(\psi)$ is in $H^{s-2}$ for s sufficiently large, So in this sense $k=2$. But $V(\psi)$ depends non-locally on $\psi$ in much the same sense as in the paper by Ginibre-Velo on non-local interaction in non-linear Schrodinger. | |
| Aug 20, 2010 at 15:08 | history | answered | Piero D'Ancona | CC BY-SA 2.5 |