Existence and decay of solutions to the two-dimensional fractional quasigeostrophic equation

This paper studies the fractional quasigeostrophic equation with modified dissipativity. We prove the global existence of weak solutions by employing the Galerkin approximation method, and when alpha is an element of (1/2, 1), the weak solution is unique. Finally, decay estimate for solutions in Sobolev norms is given. (C) 2010 American Institute of Physics. [doi:10.1063/1.3460319]