Global solutions of nonlinear Schrödinger equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
AMS
1999
|
| Series: | American Mathematical Society: Colloquium publications
46 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 182 S. |
| ISBN: | 0821819194 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Introduction and summary 1
I. An overview of results on the Cauchy problem for NLS 5
1. Equations 5
2. Wellposedness of the Cauchy problem 6
3. Scattering results 10
4. Estimates on the linear group 11
5. Solving the Cauchy problem 14
6. Derivative nonlinear Schrodinger equations 14
II. Further comments 17
1. Construction of blowup solutions for conformal NLS from the ground
state 17
2. Behaviour of higher Sobolev norms 28
3. Fourier restriction theory beyond L2 33
4. L2-concentration phenomenon 37
5. The Schrodinger maximal function 45
6. Derivative nonlinear Schrodinger equation 48
III. 3D //^-critical defocusing NLS 51
1. Consider 3D NLS 51
2. Fix a time interval / = [0, T] 51
3. Sketch of the argument 54
4. A concentration property 59
5. A version of Morawetz inequality 61
6. Construction of an appropriate time interval 63
7. Details on the perturbative analysis 66
8. A variant of the method 70
IV. Global wellposedness below energy norm 79
1. Description of the method 79
2. The example of the NLW 79
3. The case of the nonlinear Schrodinger equation 83
4. Symplectic capacities and symplectic Hilbert spaces 93
5. Global wellposedness of the NLW (4.41) 97
V. Nonlinear Schrodinger equation with periodic boundary conditions 105
1. Introduction 105
2. Results on the Cauchy problem 106
3. Periodic Strichartz inequalities 108
vii
viii CONTENTS
4. Sketch of proof of Theorems 2.1 and 2.7 109
5. Invariant Gibbs measures (ID) 122
6. Invarinat Gibbs measures (D 1) 129
7. Invariant Gibbs measures (unbounded domains) 135
8. Quasi-periodic solutions 143
Appendix 1. Growth of Sobolev norms in linear Schrodinger equations with
smooth time dependent potential 155
Appendix 2. Zakharov systems 173
References 176
Index 181
|
| any_adam_object | 1 |
| author | Bourgain, Jean 1954-2018 |
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| dewey-sort | 3515 3353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012798022 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:33:50Z |
| institution | BVB |
| isbn | 0821819194 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008703222 |
| oclc_num | 246113322 |
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| physical | VIII, 182 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | AMS |
| record_format | marc |
| series | American Mathematical Society: Colloquium publications |
| series2 | American Mathematical Society: Colloquium publications |
| spelling | Bourgain, Jean 1954-2018 Verfasser (DE-588)109854780 aut Global solutions of nonlinear Schrödinger equations J. Bourgain Providence, RI AMS 1999 VIII, 182 S. txt rdacontent n rdamedia nc rdacarrier American Mathematical Society: Colloquium publications 46 Nichtlineare Schrödinger-Gleichung - Globale Lösung Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s DE-604 Elektronische Reproduktion 978-1-4704-3192-1 American Mathematical Society: Colloquium publications 46 (DE-604)BV035417609 46 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008703222&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bourgain, Jean 1954-2018 Global solutions of nonlinear Schrödinger equations American Mathematical Society: Colloquium publications Nichtlineare Schrödinger-Gleichung - Globale Lösung Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd |
| subject_GND | (DE-588)4278277-6 |
| title | Global solutions of nonlinear Schrödinger equations |
| title_auth | Global solutions of nonlinear Schrödinger equations |
| title_exact_search | Global solutions of nonlinear Schrödinger equations |
| title_full | Global solutions of nonlinear Schrödinger equations J. Bourgain |
| title_fullStr | Global solutions of nonlinear Schrödinger equations J. Bourgain |
| title_full_unstemmed | Global solutions of nonlinear Schrödinger equations J. Bourgain |
| title_short | Global solutions of nonlinear Schrödinger equations |
| title_sort | global solutions of nonlinear schrodinger equations |
| topic | Nichtlineare Schrödinger-Gleichung - Globale Lösung Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd |
| topic_facet | Nichtlineare Schrödinger-Gleichung - Globale Lösung Nichtlineare Schrödinger-Gleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008703222&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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