Strichartz estimates and the Cauchy problem for the gravity water waves equations:
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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 1229 (fifth of 6 numbers) |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | v, 108, 4 ungezählte Seiten |
| ISBN: | 9781470432034 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Chapter 1. Introduction 1
1.1. Equations and assumptions on the fluid domain 3
1.2. Regularity thresholds for the water waves 5
1.3. Reformulation of the equations 6
1.4. Main result 6
1.5. Paradifferential reduction 7
1.6. Strichartz estimates 9
Chapter 2. Strichartz estimates 13
2.1. Symmetrization of the equations 13
2.2. Smoothing the paradifferential symbol 16
2.3. The pseudo-differential symbol 20
2.4. Several reductions 20
2.5. Straightening the vector field 22
2.6. Reduction to a semi-classical form 24
2.7. The parametrix 30
2.8. The dispersion estimate 43
2.9. The Strichartz estimates 48
Chapter 3. Cauchy problem 53
3.1. A priori estimates 53
3.2. Contraction estimates 59
3.3. Passing to the limit in the equations 68
3.4. Existence and uniqueness 71
Appendix A. Paradifferential calculus 73
A.l. Notations and classical results 73
A.2. Symbolic calculus 74
A. 3. Paraproducts and product rules 75
Appendix B. Tame estimates for the Dirichlet-Neumann operator 79
B. l. Scheme of the analysis 79
B.2. Parabolic evolution equation 82
B.3. Paralinearization 85
Appendix C. Estimates for the Taylor coefficient 93
Appendix D. Sobolev estimates 97
D.l. Introduction 97
D.2. Symmetrization of the equations 98
D.3. Sobolev estimates 98
iii
iv
CONTENTS
103
Appendix E. Proof of a technical result
Bibliography
105
|
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| author_sort | Alazard, Thomas |
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| id | DE-604.BV045468399 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:18:59Z |
| institution | BVB |
| isbn | 9781470432034 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030853556 |
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| physical | v, 108, 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 | Alazard, Thomas (DE-588)1084007835 aut Strichartz estimates and the Cauchy problem for the gravity water waves equations Thomas Alazard, Nicolas Burg, Claude Zuily Providence, Rhode Island American Mathematical Society [2018] © 2018 v, 108, 4 ungezählte Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 256, number 1229 (fifth of 6 numbers) Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd rswk-swf Ungleichung (DE-588)4139098-2 gnd rswk-swf Wasserwelle (DE-588)4136091-6 gnd rswk-swf Ungleichung (DE-588)4139098-2 s DE-604 Wasserwelle (DE-588)4136091-6 s Cauchy-Anfangswertproblem (DE-588)4147404-1 s 1\p DE-604 Burg, Nicolas aut Zuily, Claude 1945- (DE-588)1132172462 aut Memoirs of the American Mathematical Society volume 256, number 1229 (fifth of 6 numbers) (DE-604)BV008000141 1229 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=030853556&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Alazard, Thomas Burg, Nicolas Zuily, Claude 1945- Strichartz estimates and the Cauchy problem for the gravity water waves equations Memoirs of the American Mathematical Society Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Ungleichung (DE-588)4139098-2 gnd Wasserwelle (DE-588)4136091-6 gnd |
| subject_GND | (DE-588)4147404-1 (DE-588)4139098-2 (DE-588)4136091-6 |
| title | Strichartz estimates and the Cauchy problem for the gravity water waves equations |
| title_auth | Strichartz estimates and the Cauchy problem for the gravity water waves equations |
| title_exact_search | Strichartz estimates and the Cauchy problem for the gravity water waves equations |
| title_full | Strichartz estimates and the Cauchy problem for the gravity water waves equations Thomas Alazard, Nicolas Burg, Claude Zuily |
| title_fullStr | Strichartz estimates and the Cauchy problem for the gravity water waves equations Thomas Alazard, Nicolas Burg, Claude Zuily |
| title_full_unstemmed | Strichartz estimates and the Cauchy problem for the gravity water waves equations Thomas Alazard, Nicolas Burg, Claude Zuily |
| title_short | Strichartz estimates and the Cauchy problem for the gravity water waves equations |
| title_sort | strichartz estimates and the cauchy problem for the gravity water waves equations |
| topic | Cauchy-Anfangswertproblem (DE-588)4147404-1 gnd Ungleichung (DE-588)4139098-2 gnd Wasserwelle (DE-588)4136091-6 gnd |
| topic_facet | Cauchy-Anfangswertproblem Ungleichung Wasserwelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030853556&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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