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Local Dissipation of Energy for Continuous Incompressible Euler Flows - Phillip Isett
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- 1 Intro
- 2 Motivation: Weak Solutions to the Euler equations
- 3 Motivation: Sufficiently smooth solutions conserve energy
- 4 Motivation: Hydrodynamic turbulence
- 5 Onsager and Ideal Turbulence
- 6 Motivation: Onsager's Conjecture (1949)
- 7 K41 implies compactness
- 8 K41 Folklore Conjecture for Navier-Stokes
- 9 Zero viscosity limits dissipate energy locally
- 10 K41 Folklore Conjecture in the inviscid limit
- 11 Open Problem: Strong Onsager conjecture
- 12 Theorem: First result on the Strong Onsager Conjecture
- 13 Theorem: Improvement on the Strong Onsager Conjecture
- 14 Outline
- 15 Continuous Solutions: The Euler-Reynolds Equations
- 16 Continuous Solutions: Convex Integration for Euler
- 17 The High-Frequency Correction
- 18 Micralocal Lemma
- 19 The Main Error Terms
- 20 Dissipative Euler Reynolds flow
- 21 Plan of attack
- 22 The new terms: The Transport term
- 23 Getting rid of the unresolved flux density
- 24 Conflict: Eliminate the Unresolved Flux Current and Stress
- 25 Dangerous terms: algebraic cancellation saving the day
