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THE QUASI-GEOSTROPHIC EQUATION AND ITS TWO REGULARIZATIONS

ABSTRACT We consider the quasi-geostrophic model and its two different regularizations. Global regularity results are established for the regularized models with critical or sub-critical indices. The proof[4], [13] of Onsager's conjecture[19] concerning weak solutions of the 3D Euler equations and the notion of dissipative solutions of Duchon and Robert[12] are extended to weak solutions of the quasi-geostrophic equation.