MARC details
| 000 -LEADER |
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| fixed length control field |
02774cam a22003497 4500 |
| 001 - CONTROL NUMBER |
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| control field |
on1432712088 |
| 003 - CONTROL NUMBER IDENTIFIER |
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OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20240624111422.0 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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| fixed length control field |
240507s2024 riu 0|| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
1470469790 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9781470469795 |
| 035 ## - SYSTEM CONTROL NUMBER |
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| System control number |
(OCoLC)1432712088 |
| 040 ## - CATALOGING SOURCE |
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| Original cataloging agency |
YDX |
| Language of cataloging |
eng |
| Transcribing agency |
YDX |
| Modifying agency |
OCLCO |
| -- |
YSM |
| -- |
OCLCO |
| -- |
UNBCA |
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OCLCO |
| 066 ## - CHARACTER SETS PRESENT |
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| Alternate G0 or G1 character set |
(S |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Burq, Nicolas, |
| Relator term |
author |
| 245 10 - TITLE STATEMENT |
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| Title |
Almost sure scattering for the one dimensional nonlinear Schrödinger equation / |
| Statement of responsibility, etc. |
Nicolas Burq, Laurent Thomann |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
Providence, RI : |
| Name of producer, publisher, distributor, manufacturer |
American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2024. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Date of production, publication, distribution, manufacture, or copyright notice |
©2024 |
| 300 ## - PHYSICAL DESCRIPTION |
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| Extent |
vii, 87 pages ; |
| Dimensions |
26 cm |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
unmediated |
| Media type code |
n |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
volume |
| Carrier type code |
nc |
| Source |
rdacarrier |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Memoirs of the American Mathematical Society ; |
| Volume/sequential designation |
no. 1480 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
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| Bibliography, etc. note |
Includes bibliographic references. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Scattering (Mathematics) |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Dispersion (Mathématiques) |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
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| Personal name |
Thomann, Laurent, |
| Relator term |
author |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
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| Uniform title |
Memoirs of the American Mathematical Society ; |
| Volume/sequential designation |
v. 1480. |
| 880 ## - ALTERNATE GRAPHIC REPRESENTATION |
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| Linkage |
520-00/(S |
| a |
We consider the one-dimensional nonlinear Schrödinger equation with a nonlinearity of degree p>1. On compact manifolds many probability measures are invariant by the flow of the linear Schrödinger equation (e.g. Wiener measures), and it is sometimes possible to modify them suitably and get invariant (Gibbs measures) or quasi-invariant measures for the non linear problem. On Rd, the large time dispersion shows that the only invariant measure is the δ measure on the trivial solution u=0, and the good notion to track is whether the non linear evolution of the initial measure is well described by the linear (nontrivial) evolution. This is precisely what we achieve in this work. We exhibit measures on the space of initial data for which we describe the nontrivial evolution by the linear Schrödinger flow and we show that their nonlinear evolution is absolutely continuous with respect to this linear evolution. Actually, we give precise (and optimal) bounds on the Radon–Nikodym derivatives of these measures with respect to each other and we characterise their Lp regularity. We deduce from this precise description the global well-posedness of the equation for p>1 and scattering for p>3 (actually even for 1<p≤3, we get a dispersive property of the solutions and exhibit an almost sure polynomial decay in time of their Lp+1 norm). To the best of our knowledge, it is the first occurence where the description of quasi-invariant measures allows to get quantitative asymptotics (here scattering properties or decay) for the nonlinear evolution. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Books |
| Suppress in OPAC |
No |
| 948 ## - LOCAL PROCESSING INFORMATION (OCLC); SERIES PART DESIGNATOR (RLIN) |
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| h (OCLC) |
NO HOLDINGS IN P5A - 7 OTHER HOLDINGS |
