- Title Pages
- Preface
- Introduction
-
1 The Euler-Reynolds 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 High-High 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 Transport-Elliptic Estimates - Appendices
- References
- Index
Accounting for the Parameters and the Problem with the High-High Term
Accounting for the Parameters and the Problem with the High-High Term
- Chapter:
- 19 Accounting for the Parameters and the Problem with the High-High Term
- 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 list of all the parameters and summarizes their current status while also discussing the problem with the High–High term. These include the parameters used to mollify the Reynolds stress in space and along the coarse scale flow, the parameter used to mollify the velocity field in space, the lifespan parameter, and the parameter used to make sure the phase functions are high frequency. In addition to the High–High term, the chapter considers the Transport term, which becomes large when a short lifespan is chosen. It also shows how the Transport term could be made to have the size required for regularity up to 1/3.
Keywords: parameters, High–High term, Reynolds stress, coarse scale flow, velocity field, lifespan parameter, phase function, Transport term, regularity
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- Title Pages
- Preface
- Introduction
-
1 The Euler-Reynolds 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 High-High 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 Transport-Elliptic Estimates - Appendices
- References
- Index
