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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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Mollification along the Coarse Scale Flow

Mollification along the Coarse Scale Flow

Chapter:
18 Mollification along the Coarse Scale Flow
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/9780691174822.003.0018

This chapter shows how to construct the appropriate mollification of the Reynolds stress along the coarse scale flow. Unlike the velocity field, which was only mollified in the spatial variables and which earned its time-regularity through the Euler-Reynolds equation, the Reynolds stress must be mollified in both space and time. Mollification along the flow is consistent with the Galilean invariance of the equations. After considering the problem of mollifying the stress in time, the chapter explains how the stress can be mollified in both space and time. It then chooses the mollification parameters, requiring that the error term generated by this mollification constitutes a small fraction of the allowable stress. It also derives estimates for the coarse scale flow as well as transport estimates for the mollified stress.

Keywords:   mollification, Reynolds stres, coarse scale flow, Galilean invariance, error term, transport estimate

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