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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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Bounds for the Vector Amplitudes

Bounds for the Vector Amplitudes

Chapter:
21 Bounds for the Vector Amplitudes
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/9780691174822.003.0021

This chapter estimates the bounds for the vector amplitudes vsubscript I and wsubscript I of the correction. It first presents the proposition about deriving the estimates for the transport part of vsubscript I and proceeds by computing estimates for vsubscript I, starting with the spatial derivatives. It then introduces a second proposition dealing with spatial derivatives of vector amplitudes and a third proposition for the first material derivative of vector amplitudes. The fourth proposition is concerned with the second material derivative of the vector amplitudes. The chapter shows that all the bounds for γ‎subscript I and α‎subscript I are identical until the second material derivative. It concludes with a corollary about estimates for corrected amplitudes.

Keywords:   vector amplitude, correction, transport, spatial derivative, first material derivative, second material derivative

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