Jump to ContentJump to Main Navigation
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time$
Users without a subscription are not able to see the full content.

Philip Isett

Print publication date: 2017

Print ISBN-13: 9780691174822

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691174822.001.0001

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 25 June 2022

Transport Estimates

Transport Estimates

17 Transport Estimates
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Philip Isett

Princeton University Press

This chapter derives estimates for quantities which are transported by the coarse scale flow and for their derivatives. It first considers the phase functions which satisfy the Transport equation, with the goal of choosing the lifespan parameter τ‎ sufficiently small so that all the phase functions which appear in the analysis can be guaranteed to remain nonstationary in the time interval, and so that the Stress equation can be solved. In order for these requirements to be met, τ‎ small enough is chosen so that the gradients of the phase functions do not depart significantly from their initial configurations. The chapter presents a proposition that bounds the separation of the phase gradients from their initial values in terms of b (b is less than or equal to 1, a form related to τ‎). Finally, it gathers estimates for relative velocity and relative acceleration.

Keywords:   coarse scale flow, phase function, Transport equation, lifespan parameter, Stress equation, phase gradient, relative velocity, relative acceleration

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.