Global regularity for 2D water waves with surface tension:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2018]
|
| Series: | Memoirs of the American Mathematical Society
volume 256, number 1227 (third of 6 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | v, 123, 4 ungezählte Seiten |
| ISBN: | 9781470431037 |
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MARC
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| 245 | 1 | 0 | |a Global regularity for 2D water waves with surface tension |c Alexandru D. Ionescu, Fabio Pusateri |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [2018] | |
| 264 | 4 | |c © 2018 | |
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. Free boundary Euler equations and water waves 1
1.2. The main results 2
1.3. Main ideas of the proof 4
1.4. Paralinearization and the Dirichlet-Neumann operator 5
1.5. Energy estimates and quartic energy inequalities 6
1.6. Compatible vector-field structures 9
1.7. Decay and modified scattering 10
1.8. Organization 11
Chapter 2. Preliminaries 13
2.1. Notation and basic lemmas 13
2.2. The main proposition 16
Chapter 3. Derivation of the main scalar equation 17
3.1. Symmetrization of the equations 19
3.2. Higher order derivatives and weights 24
Chapter 4. Energy estimates I: high Sobolev estimates 27
4.1. The higher order energy functional 27
4.2. Analysis of the symbols and proof of Lemma 4.2 28
4.3. Proof of Lemma 4.3 29
Chapter 5. Energy estimates II: low frequencies 39
5.1. The basic low frequency energy 39
5.2. The cubic low frequency energy 39
5.3. Analysis of the symbols and proof of Lemma 5.2 40
5.4. Proof of Lemma 5.3 41
Chapter 6. Energy estimates III: Weighted estimates for high frequencies 45
6.1. The weighted energy functionals 45
6.2. Analysis of the symbols and proof of Lemma 6.2 46
6.3. Proof of Lemma 6.3 47
Chapter 7. Energy estimates IV: Weighted estimates for low frequencies 53
7.1. The cubic low frequency weighted energy 53
7.2. Analysis of the symbols and proof of Lemma 7.2 54
7.3. Proof of Lemma 7.3 55
Chapter 8. Decay estimates 61
8.1. Set up 61
ili
IV
CONTENTS
8.2. The “semilinear” normal form transformation 62
8.3. The profile / 65
8.4. The Z-norra and proof of Proposition 8.1 67
8.5. The equation for v and proof of Proposition 8.5 68
Chapter 9. Proof of Lemma 8.6 73
9.1. Proof of (9.6) 75
9.2. Proof of (9.7) 79
9.3. Proof of (9.8) 81
Chapter 10. Modified scattering 87
Appendix A. Analysis of symbols 93
A.l. Notation 93
A. 2. Quadratic symbols 93
Appendix B. The Dirichlet-Neumann operator 97
B. l. The perturbed Hilbert transform and proof of Proposition B.l 98
B. 2. Proof of Lemma B.3 103
Appendix C. Elliptic bounds 111
C. l. The spaces OmjQ; 111
C.2. Linear, quadratic, and cubic bounds 113
C.3. Semilinear expansions 117
Bibliography 121
|
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| author | Ionescu, Alexandru Dan 1973- Pusateri, Fabio 1983- |
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| id | DE-604.BV045468269 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:18:59Z |
| institution | BVB |
| isbn | 9781470431037 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030853428 |
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| physical | v, 123, 4 ungezählte Seiten |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Ionescu, Alexandru Dan 1973- (DE-588)1051220254 aut Global regularity for 2D water waves with surface tension Alexandru D. Ionescu, Fabio Pusateri Providence, Rhode Island American Mathematical Society [2018] © 2018 v, 123, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 256, number 1227 (third of 6 numbers) Oberflächenspannung (DE-588)4139720-4 gnd rswk-swf Wasserwelle (DE-588)4136091-6 gnd rswk-swf Kapillarität (DE-588)4029556-4 gnd rswk-swf Wasserwelle (DE-588)4136091-6 s DE-604 Kapillarität (DE-588)4029556-4 s Oberflächenspannung (DE-588)4139720-4 s Pusateri, Fabio 1983- (DE-588)1176682989 aut Memoirs of the American Mathematical Society volume 256, number 1227 (third of 6 numbers) (DE-604)BV008000141 1227 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030853428&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ionescu, Alexandru Dan 1973- Pusateri, Fabio 1983- Global regularity for 2D water waves with surface tension Memoirs of the American Mathematical Society Oberflächenspannung (DE-588)4139720-4 gnd Wasserwelle (DE-588)4136091-6 gnd Kapillarität (DE-588)4029556-4 gnd |
| subject_GND | (DE-588)4139720-4 (DE-588)4136091-6 (DE-588)4029556-4 |
| title | Global regularity for 2D water waves with surface tension |
| title_auth | Global regularity for 2D water waves with surface tension |
| title_exact_search | Global regularity for 2D water waves with surface tension |
| title_full | Global regularity for 2D water waves with surface tension Alexandru D. Ionescu, Fabio Pusateri |
| title_fullStr | Global regularity for 2D water waves with surface tension Alexandru D. Ionescu, Fabio Pusateri |
| title_full_unstemmed | Global regularity for 2D water waves with surface tension Alexandru D. Ionescu, Fabio Pusateri |
| title_short | Global regularity for 2D water waves with surface tension |
| title_sort | global regularity for 2d water waves with surface tension |
| topic | Oberflächenspannung (DE-588)4139720-4 gnd Wasserwelle (DE-588)4136091-6 gnd Kapillarität (DE-588)4029556-4 gnd |
| topic_facet | Oberflächenspannung Wasserwelle Kapillarität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030853428&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT ionescualexandrudan globalregularityfor2dwaterwaveswithsurfacetension AT pusaterifabio globalregularityfor2dwaterwaveswithsurfacetension |