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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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Constructing the Correction

Constructing the Correction

(p.30) 7 Constructing the Correction
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Philip Isett

Princeton University Press

This chapter explains how the correction is constructed, first by considering the transportation of the phase functions. A solution (v, p, R) to the Euler-Reynolds equations is fixed and a correction v₁ = v + V, p₁ = p + P is presented. Here v is an approximation to the “coarse scale velocity” since the solution ultimately achieved by the process will resemble v at a sufficiently coarse scale. The next step is to eliminate the Transport term. A time cutoff function is also introduced, where the time cutoff itself is differentiated in the Transport term. Finally, the chapter describes the High–High Interference term and Beltrami flows, how to construct the corrections Vsubscript I, P₀ in such a way that the Stress term can be reduced to a new stress, and the Stress equation and initial phase directions.

Keywords:   correction, phase function, Euler-Reynolds equations, coarse scale velocity, Transport term, time cutoff function, High–High Interference term, Beltrami flows, Stress term, Stress equation

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