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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Isett, Philip, author. aut http://id.loc.gov/vocabulary/relators/aut Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / Philip Isett. Princeton, NJ : Princeton University Press, [2017] ©2017 1 online resource (216 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 196 Frontmatter -- Contents -- Preface -- Part I. Introduction -- Part II. General Considerations of the Scheme -- Part III. Basic Construction of the Correction -- Part IV. Obtaining Solutions from the Construction -- Part V. Construction of Regular Weak Solutions: Preliminaries -- Part VI Construction of Regular Weak Solutions: Estimating the Correction -- Part VII. Construction of Regular Weak Solutions: Estimating the New Stress -- Acknowledgments -- Appendices -- References -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) SCIENCE / Physics / Mathematical & Computational. bisacsh Beltrami flows. Einstein summation convention. Euler equations. Euler flow. Euler-Reynolds equations. Euler-Reynolds system. Galilean invariance. Galilean transformation. HighЈigh Interference term. HighЈigh term. HighЌow Interaction term. Hlder norm. Hlder regularity. Lars Onsager. Main Lemma. Main Theorem. Mollification term. Newton's law. Noether's theorem. Onsager's conjecture. Reynolds stres. Reynolds stress. Stress equation. Stress term. Transport equation. Transport term. Transport-Elliptic equation. abstract index notation. algebra. amplitude. coarse scale flow. coarse scale velocity. coefficient. commutator estimate. commutator term. commutator. conservation of momentum. continuous solution. contravariant tensor. convergence. convex integration. correction term. correction. covariant tensor. dimensional analysis. divergence equation. divergence free vector field. divergence operator. energy approximation. energy function. energy increment. energy regularity. energy variation. energy. error term. error. finite time interval. first material derivative. fluid dynamics. frequencies. frequency energy levels. h-principle. integral. lifespan parameter. lower indices. material derivative. mollification. mollifier. moment vanishing condition. momentum. multi-index. non-negative function. nonzero solution. optimal regularity. oscillatory factor. oscillatory term. parameters. parametrix expansion. parametrix. phase direction. phase function. phase gradient. pressure correction. pressure. regularity. relative acceleration. relative velocity. scaling symmetry. second material derivative. smooth function. smooth stress tensor. smooth vector field. spatial derivative. stress. tensor. theorem. time cutoff function. time derivative. transport derivative. transport equations. transport estimate. transport. upper indices. vector amplitude. velocity correction. velocity field. velocity. weak limit. weak solution. Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 9783110540550 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 9783110548204 ZDB-23-DMA Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2017 9783110543322 print 9780691174839 https://doi.org/10.1515/9781400885428 https://www.degruyter.com/isbn/9781400885428 Cover https://www.degruyter.com/document/cover/isbn/9781400885428/original |
language |
English |
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eBook |
author |
Isett, Philip, Isett, Philip, |
spellingShingle |
Isett, Philip, Isett, Philip, Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Preface -- Part I. Introduction -- Part II. General Considerations of the Scheme -- Part III. Basic Construction of the Correction -- Part IV. Obtaining Solutions from the Construction -- Part V. Construction of Regular Weak Solutions: Preliminaries -- Part VI Construction of Regular Weak Solutions: Estimating the Correction -- Part VII. Construction of Regular Weak Solutions: Estimating the New Stress -- Acknowledgments -- Appendices -- References -- Index |
author_facet |
Isett, Philip, Isett, Philip, |
author_variant |
p i pi p i pi |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Isett, Philip, |
title |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / |
title_sub |
(AMS-196) / |
title_full |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / Philip Isett. |
title_fullStr |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / Philip Isett. |
title_full_unstemmed |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / Philip Isett. |
title_auth |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / |
title_alt |
Frontmatter -- Contents -- Preface -- Part I. Introduction -- Part II. General Considerations of the Scheme -- Part III. Basic Construction of the Correction -- Part IV. Obtaining Solutions from the Construction -- Part V. Construction of Regular Weak Solutions: Preliminaries -- Part VI Construction of Regular Weak Solutions: Estimating the Correction -- Part VII. Construction of Regular Weak Solutions: Estimating the New Stress -- Acknowledgments -- Appendices -- References -- Index |
title_new |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : |
title_sort |
hölder continuous euler flows in three dimensions with compact support in time : (ams-196) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2017 |
physical |
1 online resource (216 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- Preface -- Part I. Introduction -- Part II. General Considerations of the Scheme -- Part III. Basic Construction of the Correction -- Part IV. Obtaining Solutions from the Construction -- Part V. Construction of Regular Weak Solutions: Preliminaries -- Part VI Construction of Regular Weak Solutions: Estimating the Correction -- Part VII. Construction of Regular Weak Solutions: Estimating the New Stress -- Acknowledgments -- Appendices -- References -- Index |
isbn |
9781400885428 9783110540550 9783110548204 9783110494914 9783110543322 9780691174839 |
url |
https://doi.org/10.1515/9781400885428 https://www.degruyter.com/isbn/9781400885428 https://www.degruyter.com/document/cover/isbn/9781400885428/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
530 - Physics |
dewey-ones |
532 - Fluid mechanics; liquid mechanics |
dewey-full |
532.1 |
dewey-sort |
3532.1 |
dewey-raw |
532.1 |
dewey-search |
532.1 |
doi_str_mv |
10.1515/9781400885428 |
oclc_num |
968415598 |
work_keys_str_mv |
AT isettphilip holdercontinuouseulerflowsinthreedimensionswithcompactsupportintimeams196 |
status_str |
n |
ids_txt_mv |
(DE-B1597)477784 (OCoLC)968415598 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2017 |
is_hierarchy_title |
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time : (AMS-196) / |
container_title |
Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 |
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