Timeline for Failure of Strichartz estimates for the wave equation: elaboration of a counter-example
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 18, 2020 at 21:00 | comment | added | Terry Tao | Yes. In physical space this corresponds to trying to create a "sonic boom" effect by having the light cones from the sources at different times all line up. | |
| Sep 18, 2020 at 18:51 | comment | added | J.Mayol | @TerryTao thank you, your notes are nice, at least I understand a little more why the Brownian motion is needed. It seems like we can replace the Brownian motion with some $C^{1/2}$ function (with appropriate norm) and try to work with it, although this basically reduces to using the Brownian motion. One last thing: that the $-te_3$ is needed is because we want to "kill" the oscillatory factor $e^{it|\xi|}$ in order to force the integral to diverge? Am I right? | |
| Sep 18, 2020 at 18:30 | comment | added | Terry Tao | The Brownian motion term is needed to destroy an "unwanted" cancellation in the Duhamel integral that would otherwise occur if this randomization was not present. I discuss this a little in my own unpublished notes on this example at math.ucla.edu/~tao/preprints/Expository/stein.dvi | |
| Sep 18, 2020 at 15:40 | comment | added | J.Mayol | @YCor is it better now? If there is need for more details about the proof in the document I can provide them. | |
| Sep 18, 2020 at 15:39 | history | edited | J.Mayol | CC BY-SA 4.0 |
edited title
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| Sep 18, 2020 at 14:27 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading; deleted 'thanks'
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| Sep 18, 2020 at 14:23 | history | edited | J.Mayol | CC BY-SA 4.0 |
added 227 characters in body
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| Sep 18, 2020 at 14:18 | history | asked | J.Mayol | CC BY-SA 4.0 |