Timeline for Help in understanding "Local well-posedness for the Maxwell-Schrodinger system"
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Jan 30, 2015 at 9:34 | comment | added | gsa | I think MO is not the best place for such a discussion. I updated my profile so that you can find my email address. | |
| Jan 29, 2015 at 16:58 | comment | added | Sal | @gsa Maybe one reason could be that using Strichartz estimates for Klein-Gordon they get a larger range for the values of $\sigma$ of that they would obtain using energy inequality for the wave equation. | |
| Jan 28, 2015 at 18:47 | comment | added | Sal | @gsa But the wave equation has also a conservation of energy which can be used. I have to think about it, because it's not very clear to me. | |
| Jan 28, 2015 at 17:31 | comment | added | gsa | Maybe it's possible to work with the wave equation as well. But the standard Strichartz estimates for the wave equation are stated in the homogeneous Sobolev spaces $\dot{H}^{s,p}$, which are a bit delicate. My guess is that they prefer to work with the inhomogeneous spaces $H^{s,p}$ and thus use the Strichartz estimates for Klein-Gordon. | |
| Jan 28, 2015 at 8:21 | comment | added | Sal | @gsa May I ask you to clarify another doubt I have? Why do you think they use estimates for Klein-Gordon equations and not estimates for the wave equation? | |
| Jan 27, 2015 at 16:39 | comment | added | Sal | @gsa Thank you. I stopped before that lemma and I was trying to understand it with previous computations. | |
| Jan 27, 2015 at 16:25 | comment | added | gsa | They use the assumption $s\geq 5/3$ in the estimate (6.10). They apply the fractional Leibniz rule to the product in combination with the Sobolev embedding of $H^{s-1,2}$ to $L^q$ where they use $1-1/\tilde{r} = 1/2 +1/q$ and choose $\tilde{r} = 3/(4-2s)$. The Sobolev embedding then only works for $s\geq 5/3$. | |
| S Jan 27, 2015 at 14:34 | history | suggested | user25199 | CC BY-SA 3.0 |
Made title more specific, minor typos.
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| Jan 27, 2015 at 14:32 | review | Suggested edits | |||
| S Jan 27, 2015 at 14:34 | |||||
| Jan 27, 2015 at 14:31 | review | First posts | |||
| Jan 27, 2015 at 14:33 | |||||
| Jan 27, 2015 at 14:29 | history | asked | Sal | CC BY-SA 3.0 |