
Contents
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11.1 The Base Case 11.1 The Base Case
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11.2 The Main Lemma Implies the Main Theorem 11.2 The Main Lemma Implies the Main Theorem
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11.2.1 Choosing the Parameters 11.2.1 Choosing the Parameters
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11.2.2 Choosing the Energies 11.2.2 Choosing the Energies
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11.2.3 Regularity of the Velocity Field 11.2.3 Regularity of the Velocity Field
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Continuity Continuity
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Hölder Norms of the Correction Hölder Norms of the Correction
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11.2.4 Asymptotics for the Parameters 11.2.4 Asymptotics for the Parameters
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A Remark about Dimensional Analysis. A Remark about Dimensional Analysis.
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11.2.5 Regularity of the Pressure 11.2.5 Regularity of the Pressure
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11.2.6 Compact Support in Time 11.2.6 Compact Support in Time
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11.2.7 Nontriviality of the Solution 11.2.7 Nontriviality of the Solution
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11 Main Lemma Implies the Main Theorem
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Published:February 2017
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Abstract
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.
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