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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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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
DOI:10.23943/princeton/9780691174822.003.0019

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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