Hölder continuous Euler flows in three dimensions with compact support in time:
Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. In this book, Philip Isett uses the method of convex i...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
[2017]
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| Series: | Annals of Mathematics Studies
number 196 |
| Subjects: | |
| Online Access: | DE-1043 DE-1046 DE-898 DE-859 DE-860 DE-91 DE-20 DE-706 DE-739 DE-858 Volltext |
| Summary: | Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma"—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture |
| Physical Description: | 1 Online-Ressource (x, 201 Seiten) |
| ISBN: | 9781400885428 |
| DOI: | 10.1515/9781400885428 |
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| 520 | |a Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma"—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture | ||
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| isbn | 9781400885428 |
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| series | Annals of Mathematics Studies |
| series2 | Annals of Mathematics Studies |
| spelling | Isett, Philip 1986- (DE-588)1128680203 aut Hölder continuous Euler flows in three dimensions with compact support in time Philip Isett Princeton, NJ Princeton University Press [2017] © 2017 1 Online-Ressource (x, 201 Seiten) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies number 196 Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Hölder. In this book, Philip Isett uses the method of convex integration to achieve the best-known results regarding nonuniqueness of solutions and Onsager's conjecture. Focusing on the intuition behind the method, the ideas introduced now play a pivotal role in the ongoing study of weak solutions to fluid dynamics equations. The construction itself—an intricate algorithm with hidden symmetries—mixes together transport equations, algebra, the method of nonstationary phase, underdetermined partial differential equations (PDEs), and specially designed high-frequency waves built using nonlinear phase functions. The powerful "Main Lemma"—used here to construct nonzero solutions with compact support in time and to prove nonuniqueness of solutions to the initial value problem—has been extended to a broad range of applications that are surveyed in the appendix. Appropriate for students and researchers studying nonlinear PDEs, this book aims to be as robust as possible and pinpoints the main difficulties that presently stand in the way of a full solution to Onsager's conjecture Mathematik Fluid dynamics Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd rswk-swf Eulersche Formel (DE-588)4359957-6 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd rswk-swf Hölder-Stetigkeit (DE-588)4332993-7 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Hölder-Stetigkeit (DE-588)4332993-7 s Eulersche Bewegungsgleichungen (DE-588)4219070-8 s Strömungsmechanik (DE-588)4077970-1 s DE-604 Partielle Differentialgleichung (DE-588)4044779-0 s Eulersche Formel (DE-588)4359957-6 s Erscheint auch als Druck-Ausgabe 978-0-691-17482-2 Annals of Mathematics Studies number 196 (DE-604)BV040389493 196 https://doi.org/10.1515/9781400885428 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Isett, Philip 1986- Hölder continuous Euler flows in three dimensions with compact support in time Annals of Mathematics Studies Mathematik Fluid dynamics Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd Eulersche Formel (DE-588)4359957-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Hölder-Stetigkeit (DE-588)4332993-7 gnd |
| subject_GND | (DE-588)4044779-0 (DE-588)4359957-6 (DE-588)4077970-1 (DE-588)4219070-8 (DE-588)4332993-7 (DE-588)4113937-9 |
| title | Hölder continuous Euler flows in three dimensions with compact support in time |
| title_auth | Hölder continuous Euler flows in three dimensions with compact support in time |
| title_exact_search | Hölder continuous Euler flows in three dimensions with compact support in time |
| title_full | Hölder continuous Euler flows in three dimensions with compact support in time Philip Isett |
| title_fullStr | Hölder continuous Euler flows in three dimensions with compact support in time Philip Isett |
| title_full_unstemmed | Hölder continuous Euler flows in three dimensions with compact support in time Philip Isett |
| title_short | Hölder continuous Euler flows in three dimensions with compact support in time |
| title_sort | holder continuous euler flows in three dimensions with compact support in time |
| topic | Mathematik Fluid dynamics Mathematics Partielle Differentialgleichung (DE-588)4044779-0 gnd Eulersche Formel (DE-588)4359957-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Eulersche Bewegungsgleichungen (DE-588)4219070-8 gnd Hölder-Stetigkeit (DE-588)4332993-7 gnd |
| topic_facet | Mathematik Fluid dynamics Mathematics Partielle Differentialgleichung Eulersche Formel Strömungsmechanik Eulersche Bewegungsgleichungen Hölder-Stetigkeit Hochschulschrift |
| url | https://doi.org/10.1515/9781400885428 |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT isettphilip holdercontinuouseulerflowsinthreedimensionswithcompactsupportintime |