Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time / Philip Isett.
- Format:
-
- Author/Creator:
-
- Series:
-
- Language:
- English
- Subjects (All):
-
- 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:
-
- OCLC:
- 968415598
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.