Abstract
This chapter deals with Onsager's conjecture, which would be implied by a stronger form of Lemma (10.1). It considers what could be proven assuming Conjecture (10.1) by turning to Theorem 13.1, which states that for every δ > 0, there exist nontrivial weak solutions (v, p) to the Euler equations on ℝ x ³. Here the energy will increase or decrease in certain time intervals. In order to determine which Hölder norms stay under control during the iteration, the chapter observes that the bound for the spatial derivative of the corrections V and P also controls their full space-time derivative. The chapter also discusses higher regularity for the energy, written as a sum of energy increments.
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