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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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Main Lemma Implies the Main Theorem

Main Lemma Implies the Main Theorem

11 Main Lemma Implies the Main Theorem
Hölder Continuous Euler Flows in Three Dimensions with Compact Support in Time

Philip Isett

Princeton University Press

This chapter shows that the Main Lemma implies the main theorem. It proves Theorem (10.1) by inductively applying the Main Lemma in order to construct a sequence of solutions of the Euler-Reynolds system. At each stage of the induction, an energy function is chosen along with a parameter whose choice determines the growth of the frequency parameter and the decay of the energy level. A base case lemma is then established, after which the proof of the Main Theorem (10.1) is presented so that the Main Lemma implies the Main Theorem. The Main Lemma is employed to approximately prescribe the energy increment of the correction. The solution obtained at the end of the process is nontrivial.

Keywords:   correction, Main Lemma, Euler-Reynolds system, energy function, Main Theorem, energy increment

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