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

Print publication date: 2017

Print ISBN-13: 9780691174822

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691174822.001.0001

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Structure of the Book

Structure of the Book

Chapter:
2 Structure of the Book
Source:
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time
Author(s):

Philip Isett

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691174822.003.0002

This chapter provides an overview of the book's structure. Section 3 deals with the error terms which need to be controlled, whereas Part III explains some notation of the book and presents a basic construction of the correction. The goal is to clarify how the scheme can be used to construct Hölder continuous weak solutions—continuous in space and time—to the incompressible Euler equations that fail to conserve energy. Part IV shows how to iterate the construction of Part III to obtain continuous solutions to the Euler equations. It then discusses the concept of frequency energy levels, along with the Main Lemma. It also highlights some additional difficulties which arise as one approaches the optimal regularity and illustrates how these difficulties can be overcome. Parts V–VII verify all the estimates needed for the proof of the Main Lemma.

Keywords:   weak solution, error, continuous solution, Euler equations, frequency energy levels, Main Lemma, optimal regularity

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