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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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Stress Terms Not Involving Solving the Divergence Equation

Stress Terms Not Involving Solving the Divergence Equation

Chapter:
25 Stress Terms Not Involving Solving 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/9780691174822.003.0025

This chapter estimates the terms in the new stress that do not involve solving the divergence equation. These terms are the Mollification terms and the Stress term. Throughout the estimates, Bsubscript Greek Small Letter Lamda will be assumed to be some constant. After considering the Mollification term from the velocity, the chapter introduces a proposition stating that for k = 0, … , L, there exist constants Cₖ depending on Bsubscript Greek Small Letter Lamda. It then estimates the material derivative, highlighting wastefulness in the estimate, and discusses a commutator estimate suggesting that it may be important to work with frequency energy levels of order L greater than or equal to 2. Finally, it presents the Mollification term from the stress as well as estimates for the Stress term.

Keywords:   stress, divergence equation, Mollification term, Stress term, velocity, material derivative, commutator estimate, frequency energy levels

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