Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time / Philip Isett.

Format:

Book

Thesis/Dissertation

Author/Creator:

Isett, Philip, author.

Series:

Annals of mathematics studies ; Number 196.

Annals of Mathematics Studies ; 357

Language:

English

Subjects (All):

Fluid dynamics--Mathematics.

Fluid dynamics.

Physical Description:

1 online resource (214 pages).

Place of Publication:

Princeton, NJ : Princeton University Press, [2017]

Language Note:

In English.

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.

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

Notes:

Previously issued in print: 2017.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

Author's thesis (doctoral)--Princeton University, Princeton, N.J., 2013.

ISBN:

9781400885428

1400885426

OCLC:

968415598