Sobolev estimates for two dimensional gravity water waves:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Paris
Sociéte Mathématique de France
[2015]
|
| Series: | Astérisque
374 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 241 Seiten |
| ISBN: | 9782856298213 |
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MARC
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Record in the Search Index
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| adam_text | Titel: Sobolev estimates for two dimensional gravity water waves
Autor: Alazard, Thomas
Jahr: 2015
CONTENTS Introduction ..................................... 1. Description of the main results .............. 2. Properties of the Dirichlet-Ncumami operator 3. Paradifferential normal forms method ........ 4. Iterated vector fields Z ....................... 1 1 1 1 15 1. Statement of the main results ....................................... I!) 1.1. Definitions and properties of the Diriehlet-Neumami operator ....... 1!) 1.2. Main Sobolev estimate .............................................. 31 2. Estimates for the Dirichlet-Neumann operator ................... 3!) 2.1. Main results ........................................................ 40 2.2. Sharp estimates ..................................................... 43 2.3. Tame estimates ..................................................... 5(i 2.4. Paralinearization of the Dirichlet-Neumann operator ................ 5 S 2.5. Linearization of the Dirichlet-Neumann operator .................... (i() 2.6. Taylor expansions ................................................... 62 2.7. Smooth domains .................................................... 60 3. Normal form for the water waves equation ........................ 77 3.1. Quadratic approximations without losses ........................... 77 3.2. Quadratic and cubic terms in the equations ......................... 3 1 3.3. Quadratic normal form: strategy of the proof ....................... 37 3.4. Paradifferential operators ........................................... 33 3.5. The main equations ................................................. 05 3.6. System for the new unknown ........................................ 100 3.7. Energy est ¡mate ..................................................... 115 4. Commutation of the Z-field with the equations ................... 11!) 4.1. Action of t he Z-field on the Dirichlet-Neumann operator ............ 110 4.2. Other identities
..................................................... 123 4.3. Estimates for the action of iterated vector fields .................... 120 4.4. Nonlinear estimates ................................................. 142 4.5. Estimate of tho remainder terms .................................... 150
CONTKNTS viii 5. Energy estimates for the Z-field system ........................... 167 5.1. Notations ........................................................... 167 5.2. Xonnal form for t lit Z-systoms ...................................... 171 6. Appendices ............................................................ 209 A.l. Parndiffcrent ial calculus ............................................ 209 A.2. Estimates in Holder spaces ......................................... 215 A.5. Identities ........................................................... 217 A. l. Local existence results .............................................. 219 Index ...................................................................... 233 Bibliography .............................................................. 235
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| any_adam_object | 1 |
| author | Alazard, Thomas Delort, Jean-Marc 1961- |
| author_GND | (DE-588)1084007835 (DE-588)1027794106 |
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| author_sort | Alazard, Thomas |
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| bvnumber | BV043400784 |
| classification_rvk | SK 540 SI 832 |
| ctrlnum | (OCoLC)936207249 (DE-599)BSZ454846029 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV043400784 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:24:58Z |
| institution | BVB |
| isbn | 9782856298213 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028819300 |
| oclc_num | 936207249 |
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| physical | VIII, 241 Seiten |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Sociéte Mathématique de France |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spelling | Alazard, Thomas Verfasser (DE-588)1084007835 aut Sobolev estimates for two dimensional gravity water waves Thomas Alazard and Jean-Marc Delort Paris Sociéte Mathématique de France [2015] VIII, 241 Seiten txt rdacontent n rdamedia nc rdacarrier Astérisque 374 Delort, Jean-Marc 1961- Verfasser (DE-588)1027794106 aut Astérisque 374 (DE-604)BV002579439 374 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028819300&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alazard, Thomas Delort, Jean-Marc 1961- Sobolev estimates for two dimensional gravity water waves Astérisque |
| title | Sobolev estimates for two dimensional gravity water waves |
| title_auth | Sobolev estimates for two dimensional gravity water waves |
| title_exact_search | Sobolev estimates for two dimensional gravity water waves |
| title_full | Sobolev estimates for two dimensional gravity water waves Thomas Alazard and Jean-Marc Delort |
| title_fullStr | Sobolev estimates for two dimensional gravity water waves Thomas Alazard and Jean-Marc Delort |
| title_full_unstemmed | Sobolev estimates for two dimensional gravity water waves Thomas Alazard and Jean-Marc Delort |
| title_short | Sobolev estimates for two dimensional gravity water waves |
| title_sort | sobolev estimates for two dimensional gravity water waves |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028819300&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
| work_keys_str_mv | AT alazardthomas sobolevestimatesfortwodimensionalgravitywaterwaves AT delortjeanmarc sobolevestimatesfortwodimensionalgravitywaterwaves |