Local Dissipation of Energy for Continuous Incompressible Euler Flows - Phillip Isett

Local Dissipation of Energy for Continuous Incompressible Euler Flows - Phillip Isett

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Intro

1 of 25

1 of 25

Intro

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Local Dissipation of Energy for Continuous Incompressible Euler Flows - Phillip Isett

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

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