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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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Terms Involving the Divergence Equation

Terms Involving the Divergence Equation

Chapter:
(p.175) 26 Terms Involving the Divergence Equation
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/9780691174822.003.0026

This chapter estimates the terms in the stress which involve solving a divergence equation of the form ∂ⱼQsuperscript jl = Usuperscript l = esuperscript iGreek Small Letter Lamda Greek Small Letter Xiusuperscript l. These terms are the High–Low Interaction term, the main High–High terms, the remainder of the High–High terms, and the Transport term. For each of these factors, the parametrix expansion for the divergence equation is used. The error of the expansion is eliminated by solving the divergence equation. The chapter also considers the bounds which are obeyed for the parametrices of the oscillatory terms and concludes by applying the parametrix.

Keywords:   stress, divergence equation, High–Low Interaction term, High–High term, Transport term, parametrix expansion, error, oscillatory term

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