 Title Pages
 Preface
 Introduction

1 The EulerReynolds System 
Part II General Considerations of the Scheme 
2 Structure of the Book 
3 Basic Technical Outline 
4 Notation 
5 A Main Lemma for Continuous Solutions 
6 The Divergence Equation 
7 Constructing the Correction 
8 Constructing Continuous Solutions 
9 Frequency and Energy Levels 
10 The Main Iteration Lemma 
11 Main Lemma Implies the Main Theorem 
12 Gluing Solutions 
13 On Onsager's Conjecture 
14 Preparatory Lemmas 
15 The Coarse Scale Velocity 
16 The Coarse Scale Flow and Commutator Estimates 
17 Transport Estimates 
18 Mollification along the Coarse Scale Flow 
19 Accounting for the Parameters and the Problem with the HighHigh Term 
Part VI Construction of Regular Weak Solutions: Estimating the Correction 
20 Bounds for Coefficients from the Stress Equation 
21 Bounds for the Vector Amplitudes 
22 Bounds for the Corrections 
23 Energy Approximation 
24 Checking Frequency Energy Levels for the Velocity and Pressure 
Part VII Construction of Regular Weak Solutions: Estimating the New Stress 
25 Stress Terms Not Involving Solving the Divergence Equation 
26 Terms Involving the Divergence Equation 
27 TransportElliptic Estimates  Appendices
 References
 Index
Basic Technical Outline
Basic Technical Outline
 Chapter:
 3 Basic Technical Outline
 Source:
 Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time
 Author(s):
Philip Isett
 Publisher:
 Princeton University Press
This chapter provides a more technical outline of the construction, starting with a solution to the EulerReynolds system and a correction v₁ = v + V, p₁ = p + P. The correction V is a divergence free vector field which oscillates rapidly compared to v. In the construction, there will always be a bounded number of waves Vsubscript I (at most 192) which are nonzero at any given time t. Each individual wave Vsubscript I composing V is a complexvalued, divergence free vector field that oscillates rapidly in only one direction. The chapter introduces several ways in which to represent each Vsubscript I. Finally, it presents five main error terms: the Transport term, the High–Low Interaction term, the High–High Interference terms, the Stress term, and the Mollification terms.
Keywords: error, EulerReynolds system, correction, divergence free vector field, Transport term, High–Low Interaction term, High–High Interference term, Stress term, Mollification term
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 Title Pages
 Preface
 Introduction

1 The EulerReynolds System 
Part II General Considerations of the Scheme 
2 Structure of the Book 
3 Basic Technical Outline 
4 Notation 
5 A Main Lemma for Continuous Solutions 
6 The Divergence Equation 
7 Constructing the Correction 
8 Constructing Continuous Solutions 
9 Frequency and Energy Levels 
10 The Main Iteration Lemma 
11 Main Lemma Implies the Main Theorem 
12 Gluing Solutions 
13 On Onsager's Conjecture 
14 Preparatory Lemmas 
15 The Coarse Scale Velocity 
16 The Coarse Scale Flow and Commutator Estimates 
17 Transport Estimates 
18 Mollification along the Coarse Scale Flow 
19 Accounting for the Parameters and the Problem with the HighHigh Term 
Part VI Construction of Regular Weak Solutions: Estimating the Correction 
20 Bounds for Coefficients from the Stress Equation 
21 Bounds for the Vector Amplitudes 
22 Bounds for the Corrections 
23 Energy Approximation 
24 Checking Frequency Energy Levels for the Velocity and Pressure 
Part VII Construction of Regular Weak Solutions: Estimating the New Stress 
25 Stress Terms Not Involving Solving the Divergence Equation 
26 Terms Involving the Divergence Equation 
27 TransportElliptic Estimates  Appendices
 References
 Index