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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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Basic Technical Outline

Basic Technical Outline

3 Basic Technical Outline
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Philip Isett

Princeton University Press

This chapter provides a more technical outline of the construction, starting with a solution to the Euler-Reynolds system and a correction v₁ = v + V, p₁ = p + P. The correction V is a divergence free vector field which oscillates rapidly compared to v. In the construction, there will always be a bounded number of waves Vsubscript I (at most 192) which are nonzero at any given time t. Each individual wave Vsubscript I composing V is a complex-valued, divergence free vector field that oscillates rapidly in only one direction. The chapter introduces several ways in which to represent each Vsubscript I. Finally, it presents five main error terms: the Transport term, the High–Low Interaction term, the High–High Interference terms, the Stress term, and the Mollification terms.

Keywords:   error, Euler-Reynolds system, correction, divergence free vector field, Transport term, High–Low Interaction term, High–High Interference term, Stress term, Mollification term

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