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A Main Lemma for Continuous Solutions

Philip Isett

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

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0005
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter introduces the Main Lemma that implies the existence of continuous solutions. According to this lemma, there exist constants K and C such that the following holds: Let ϵ‎ > 0, and ... More


Constructing Continuous Solutions

Philip Isett

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

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0008
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter demonstrates how the preceding construction, combined with a few estimates from Part V, can be used to prove the Main Lemma for continuous solutions. The first step is to mollify the ... More


Gluing Solutions

Philip Isett

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

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0012
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if ... More


Structure of the Book

Philip Isett

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

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0002
Subject:
Mathematics, Computational Mathematics / Optimization

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 ... More


The Divergence Equation

Philip Isett

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

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691174822
eISBN:
9781400885428
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691174822.003.0006
Subject:
Mathematics, Computational Mathematics / Optimization

This chapter introduces the divergence equation. A key ingredient in the proof of the Main Lemma for continuous solutions is to find special solutions to this divergence equation, which includes a ... More


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