Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Name: Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time
Brand: Princeton University Press
Availability: OutOfStock
Rating: 5 (1 reviews)

By Philip Isett

0 - Default Title

Description

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.

Product details

Edition:

1

Number of Pages:

216

Release Date:

2017-02-21

Publication Date:

2017-02-21

Publisher:

Princeton University Press

Languages:

Original: English

ISBN10:

0691174822

ISBN13:

9780691174822

GPSR Manufacturer Reference:

[email protected]

Weight:

431 g

Height:

157 cm

Width:

239 cm

Thickness:

18 cm

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