| Abstract: |
| The Hamiltonian of the surface quasi-geostrophic (SQG) equation is an invariant quantity for regular enough solutions. It is postulated that the critical Holder regularity required to have the Hamiltonian conserved is C^{0}, known as the Onsager type of conjecture for SQG. We give a proof of this conjecture using a two-step scheme of convex integration. |
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