Global Existence, Hamiltonian Conservation and Vanishing Viscosity for the Surface Quasi-Geostrophic Equation

Luigi De Rosa, Mickaël Latocca, Jaemin Park

For any initial datum $\hat{I}{¸}_0\in L_x^{\frac{4}{3}}$ it is proved the existence of a global-in-time weak solution $\hat{I}¸\in L_t^{\infty }{L}_x^{\frac{4}{3}}$ to the surface quasi-geostrophic equ…