Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : : (AMS-196) / / Philip Isett.
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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| Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2017] ©2017 |
| Year of Publication: | 2017 |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
196 |
| Online Access: | |
| Physical Description: | 1 online resource (216 p.) |
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| LEADER | 08446nam a22020535i 4500 | ||
|---|---|---|---|
| 001 | 9781400885428 | ||
| 003 | DE-B1597 | ||
| 005 | 20220131112047.0 | ||
| 006 | m|||||o||d|||||||| | ||
| 007 | cr || |||||||| | ||
| 008 | 220131t20172017nju fo d z eng d | ||
| 019 | |a (OCoLC)979595921 | ||
| 020 | |a 9781400885428 | ||
| 024 | 7 | |a 10.1515/9781400885428 |2 doi | |
| 035 | |a (DE-B1597)477784 | ||
| 035 | |a (OCoLC)968415598 | ||
| 040 | |a DE-B1597 |b eng |c DE-B1597 |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a nju |c US-NJ | ||
| 072 | 7 | |a SCI040000 |2 bisacsh | |
| 082 | 0 | 4 | |a 532.1 |2 23 |
| 100 | 1 | |a Isett, Philip, |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : |b (AMS-196) / |c Philip Isett. |
| 264 | 1 | |a Princeton, NJ : |b Princeton University Press, |c [2017] | |
| 264 | 4 | |c ©2017 | |
| 300 | |a 1 online resource (216 p.) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 0 | |a Annals of Mathematics Studies ; |v 196 | |
| 505 | 0 | 0 | |t Frontmatter -- |t Contents -- |t Preface -- |t Part I. Introduction -- |t Part II. General Considerations of the Scheme -- |t Part III. Basic Construction of the Correction -- |t Part IV. Obtaining Solutions from the Construction -- |t Part V. Construction of Regular Weak Solutions: Preliminaries -- |t Part VI Construction of Regular Weak Solutions: Estimating the Correction -- |t Part VII. Construction of Regular Weak Solutions: Estimating the New Stress -- |t Acknowledgments -- |t Appendices -- |t References -- |t Index |
| 506 | 0 | |a restricted access |u http://purl.org/coar/access_right/c_16ec |f online access with authorization |2 star | |
| 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. | ||
| 530 | |a Issued also in print. | ||
| 538 | |a Mode of access: Internet via World Wide Web. | ||
| 546 | |a In English. | ||
| 588 | 0 | |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) | |
| 650 | 7 | |a SCIENCE / Physics / Mathematical & Computational. |2 bisacsh | |
| 653 | |a Beltrami flows. | ||
| 653 | |a Einstein summation convention. | ||
| 653 | |a Euler equations. | ||
| 653 | |a Euler flow. | ||
| 653 | |a Euler-Reynolds equations. | ||
| 653 | |a Euler-Reynolds system. | ||
| 653 | |a Galilean invariance. | ||
| 653 | |a Galilean transformation. | ||
| 653 | |a HighЈigh Interference term. | ||
| 653 | |a HighЈigh term. | ||
| 653 | |a HighЌow Interaction term. | ||
| 653 | |a Hlder norm. | ||
| 653 | |a Hlder regularity. | ||
| 653 | |a Lars Onsager. | ||
| 653 | |a Main Lemma. | ||
| 653 | |a Main Theorem. | ||
| 653 | |a Mollification term. | ||
| 653 | |a Newton's law. | ||
| 653 | |a Noether's theorem. | ||
| 653 | |a Onsager's conjecture. | ||
| 653 | |a Reynolds stres. | ||
| 653 | |a Reynolds stress. | ||
| 653 | |a Stress equation. | ||
| 653 | |a Stress term. | ||
| 653 | |a Transport equation. | ||
| 653 | |a Transport term. | ||
| 653 | |a Transport-Elliptic equation. | ||
| 653 | |a abstract index notation. | ||
| 653 | |a algebra. | ||
| 653 | |a amplitude. | ||
| 653 | |a coarse scale flow. | ||
| 653 | |a coarse scale velocity. | ||
| 653 | |a coefficient. | ||
| 653 | |a commutator estimate. | ||
| 653 | |a commutator term. | ||
| 653 | |a commutator. | ||
| 653 | |a conservation of momentum. | ||
| 653 | |a continuous solution. | ||
| 653 | |a contravariant tensor. | ||
| 653 | |a convergence. | ||
| 653 | |a convex integration. | ||
| 653 | |a correction term. | ||
| 653 | |a correction. | ||
| 653 | |a covariant tensor. | ||
| 653 | |a dimensional analysis. | ||
| 653 | |a divergence equation. | ||
| 653 | |a divergence free vector field. | ||
| 653 | |a divergence operator. | ||
| 653 | |a energy approximation. | ||
| 653 | |a energy function. | ||
| 653 | |a energy increment. | ||
| 653 | |a energy regularity. | ||
| 653 | |a energy variation. | ||
| 653 | |a energy. | ||
| 653 | |a error term. | ||
| 653 | |a error. | ||
| 653 | |a finite time interval. | ||
| 653 | |a first material derivative. | ||
| 653 | |a fluid dynamics. | ||
| 653 | |a frequencies. | ||
| 653 | |a frequency energy levels. | ||
| 653 | |a h-principle. | ||
| 653 | |a integral. | ||
| 653 | |a lifespan parameter. | ||
| 653 | |a lower indices. | ||
| 653 | |a material derivative. | ||
| 653 | |a mollification. | ||
| 653 | |a mollifier. | ||
| 653 | |a moment vanishing condition. | ||
| 653 | |a momentum. | ||
| 653 | |a multi-index. | ||
| 653 | |a non-negative function. | ||
| 653 | |a nonzero solution. | ||
| 653 | |a optimal regularity. | ||
| 653 | |a oscillatory factor. | ||
| 653 | |a oscillatory term. | ||
| 653 | |a parameters. | ||
| 653 | |a parametrix expansion. | ||
| 653 | |a parametrix. | ||
| 653 | |a phase direction. | ||
| 653 | |a phase function. | ||
| 653 | |a phase gradient. | ||
| 653 | |a pressure correction. | ||
| 653 | |a pressure. | ||
| 653 | |a regularity. | ||
| 653 | |a relative acceleration. | ||
| 653 | |a relative velocity. | ||
| 653 | |a scaling symmetry. | ||
| 653 | |a second material derivative. | ||
| 653 | |a smooth function. | ||
| 653 | |a smooth stress tensor. | ||
| 653 | |a smooth vector field. | ||
| 653 | |a spatial derivative. | ||
| 653 | |a stress. | ||
| 653 | |a tensor. | ||
| 653 | |a theorem. | ||
| 653 | |a time cutoff function. | ||
| 653 | |a time derivative. | ||
| 653 | |a transport derivative. | ||
| 653 | |a transport equations. | ||
| 653 | |a transport estimate. | ||
| 653 | |a transport. | ||
| 653 | |a upper indices. | ||
| 653 | |a vector amplitude. | ||
| 653 | |a velocity correction. | ||
| 653 | |a velocity field. | ||
| 653 | |a velocity. | ||
| 653 | |a weak limit. | ||
| 653 | |a weak solution. | ||
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE COMPLETE 2017 |z 9783110540550 |o ZDB-23-DGG |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t EBOOK PACKAGE Mathematics 2017 |z 9783110548204 |o ZDB-23-DMA |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton Annals of Mathematics eBook-Package 1940-2020 |z 9783110494914 |o ZDB-23-PMB |
| 773 | 0 | 8 | |i Title is part of eBook package: |d De Gruyter |t Princeton University Press Complete eBook-Package 2017 |z 9783110543322 |
| 776 | 0 | |c print |z 9780691174839 | |
| 856 | 4 | 0 | |u https://doi.org/10.1515/9781400885428 |
| 856 | 4 | 0 | |u https://www.degruyter.com/isbn/9781400885428 |
| 856 | 4 | 2 | |3 Cover |u https://www.degruyter.com/document/cover/isbn/9781400885428/original |
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