CaltechAUTHORS
  A Caltech Library Service

Hölder continuous Euler flows in three dimensions with compact support in time

Isett, Philip (2017) Hölder continuous Euler flows in three dimensions with compact support in time. Annals of Mathematics Studies. Vol.196. Princeton University Press , Princeton, NJ. ISBN 978-0-691-17483-9. http://resolver.caltech.edu/CaltechAUTHORS:20180702-123946440

[img] PDF (Table of Contents) - Published Version
See Usage Policy.

116Kb
[img] PDF (Introduction) - Published Version
See Usage Policy.

361Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20180702-123946440

Abstract

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.


Item Type:Book
Related URLs:
URLURL TypeDescription
https://press.princeton.edu/titles/11045.htmlPublisherBook Publisher
Additional Information:© 2017 Princeton University Press.
Record Number:CaltechAUTHORS:20180702-123946440
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180702-123946440
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:87520
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Jul 2018 22:36
Last Modified:02 Jul 2018 22:36

Repository Staff Only: item control page